Math Forum - Problem of the Week
Submissions for Canadian Soccer
Student Short Answer Long Answer
Student 1
Each players run 1.68
kilometers.
When the players start and go to the first point they run 100
meters. I relised that because in the feild was a right triangle.
The right triangle is 1,3, and to 2. 5 to 3 is 120. Half of that is
60. Also 3 to 2 already says it is 80 meters long. Then I used the
Pythagorem Thearom to find the hypotenuse of the right triangle.
With the work I did the Hypotenuse is 100 meters long. So 1 to 2
is 100m and so start to 1. Then I calculated how long they ran and
they ran 560 meters. But they ran around 3 times. Then I times
560*3=1680m. Then to turn my answer to km I knew 1000m=1km. Which
then my answer was 1.68.
Student 2
The answer for this
problem I got is 144.2
by using a scientific
term.
Directions: s= squared
Dear
To Whom It May Concern,
I thought that the problem was kind of easy because my science
already taught us the equation to use for this but I’m not sure if I
got the answer correct. Anyways I tried to do it but first I asked
myself the question,” How much piece of information do I have in
order to complete this problem?" So I went on to collect the info.
And I got this:
•
To find the answer I need to use Pythagorean Theorem
equation, which is A2+B2=C2 (the 2 stands for the square).
•
I also now that field’s length is 120 meters and the width of
80 meters.
•
Also during the practice session the players run the Double V
three times.
•
Before the players run, they start their race at the
southwest corner of t he field, run to the top diagonal line, then go
to the southeast corner completing the first V and ht second V takes
them to the bottom of the center line and the non to the northwest
corner, finishing that off by sprinting back to the southwest corner.
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Page 1 of 14
~ So now I know my facts of the problem. So I go on and try to
figure out the problem. I know the Pythagorean Theorem equation,
which is A2+B2=C2 (the 2 stands for the square). I take a piece of
paper and set my problem:
•
As+Bs=Cs
I then fill in the numbers for the second step.
•
120s +80s=Cs
I got the second step done so I move on to the other step. The next
step I figure out the number which was squared by the equation.
•
•
•
120s = 14,400
80s = 6,400
14,400 + 6,400 = Cs
I did that step but the step after that is very important because if
you don’t get the addition rite than you won’t come up with the right
answer.
•
•
14,400 + 6,400 = 20,800
20,800 = Cs
Now I did all the steps but I only have one most important step left
that is to square root the answer I got for the addition.
Student 3
i don't have a solution.
Student 4
i did not come up with
a solution
I dont have a answer
Student 5
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•
Cs = 144.2
I got the answer of 144.2 by doing these steps and I hope I get it
right. This was kind of fun also because I got to learn new stuff and
I am aslo very into sports.
i did not understand this problem. so therefore i didn't do the problem. so i do not have an
answer.
i did not understand this problem of the week.
I didn't get this problem so I dont have an answer
Page 2 of 14
Student 6
Student 7
Student 8
I use the pythagorean
theorem a2+b2=c2
which equals 10,000
but I forgot to square
and add it together
I entered the problem
by multiplying the
length and the width
of the soccer feild and
then i divided the sides
of the field.
?
i multiplied 60*60 then i multiplied 80*80 then added it together and got 10,000 then i
squared it and got 100 so i knew that the diagonal eqaled 100 so since it was 4 lines
going diagnol i multiplied 4 times 100 and since it was 2 80 lines i multiplied 80 by 2 and
added 160 and 400
120+80/4x4
in the problem it says the length of the whole field was 120 and the width 80. Since they
run from a corner of the field to the center, i divided 120 by 2 which is 60. i then
multiplyed 60x60 (A squared) and 80x80 (B squared) then added them to find the length
they ran (C squared) i came to:
60x60=3600
80x80=6400
3600+6400=10000
Student 9
1.68
Student 10
Student 12
what I did was I i
mulltiplied to the
second power
The answer that i
came up with is 1.68
kilometers.
16.8
Student 13
16.8
Student 14
Each player will run a
distance of 1.68
Student 11
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now this is as far as i could get. im pretty sure i have to find the square root of 10000 and
then multiply that times 4 (the lines they ran) + 80 + 80 (the two sides they ran)= the full
length they ran.
I multiplied 60 times 2 and and then times 8.
1.68
I got the answer by dividing the 80 meters by how times they went around the triangles.
i got that answer by multiplying and divdceding and i use the forlum and thats how i got the
answer 16.8
i got that answer by multiplying and divdceding and i use the forlum and thats how i got the
answer 16.8
The first thing I did to get my answer was, didvide the 80 kilometers by how many times they
went around each triangle.
Page 3 of 14
Student 15
Student 16
Student 17
kilometers.
1.68 km is my answer
for the Canadian
Soccer
1.68 km is my final
answer for Canadian
Soccer.
My answer came out
to be 13.3 kilometers
each player runs.
Student 18
14.4 c2
Student 19
For my final solution I
got 0.432
Student 20
The answer to the
problem of the week
for Canadian Soccer is
144.2
I forget how I got the answer, but on the paper the answer was on the paper. The answer is
1..68km.
I just multiplied a exponent 2 and b exponent 2 and multiplied it with the number 120 and
80. I got 1.68.
I think i got the right answer.
.first i drew the pythagorean then i wrote down the information i know like how the
length is 120 meters and the width is 80 meters. .Next i tried to figure out the direction
of the double v run so i follow the double v.then i muliplyed 120 times 80 which equals
9600 divide that in to 2 and get 4800 divided that in to 3 to get 1600 =400/5=80/
6=13.3
So my answer would be 13.3 kilometers each plaqyer will run
I used the Pythagorean theoren a2+b2+=c2 then i took 120 meters and
made it 120 to
the secound power and did the same to 80 and made it 80 to the
secound power .Then i
add 120to the secound power and 80 to the secound power=c2. Then i
got 14,400+6,400
and that = c2. then when you add them together you get 20,800k=c2. So
c2 divided 144
and divided that by 2 = 14.4=c2.
its the length of the triangle that has one leg equal.
First I did 120 squared + 80 squared and then I mulitplied 120 times 120 and 80 times 80
and then I got 14400+6400. Then I added those two together and I got 20800 and I got
that I had to figure out the square root of 20800 and I got 144.2 and I rounded it to 144.
After that I mulitiplied 144 times 3 because in the problem it said that they ran the Double
V 3 times. So after I multiplied those two numbers I got 432 and then I divided it by 1000
because there is 1000 meters in each kilometer, and then that's how I got my answer of
0.432.
I understand that the students have to run a Double V Pattern, and the feild is120 meters
in length and 80 meters in width.
I didn't understand why thay wanted us to use a diagram to solve the problem instead of
using the pythagorean theorem
At first I thought I wouldn't use the diagram . I solved the problem by using the
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Page 4 of 14
Student 21
each player runs 0.432
kilometers.
Student 22
For my answer I got
3.1200
Student 23
the answer we got is
1.68kilometers per
person we rounded it
to 2 kilometers.
pythagorean theorem. I used a square as 120 and b square as 80 and I got c square as
144.2.
first i took the pythagorean theorem a squared plus b squared equals c squared. a equals
120 to the second power and equals 14400. b equals 80 to the second power anmd equals
6400. i added both them both together and got 20,800. then i found the sqAURE root of
20,800 and got 144.2. then I rounded it and got 144. then i mulitipled 144 by 3 and got
432. i times it by 3 because of the # of times they went around the the double v. then i
divied 432 into a 1000.i dived it into 1ooo becuase 1000 eqUALS ONE KILOMETER.then i
got 0.432.so each player runs 0.432 kilometers.
First I took 120 to the second power and I got 14400 And then I put 80 to the second
power and I got 6400 theen I took 14400 add it to 6400 then my answer came out to
20800 then I took the number and the divded the two into it and got the answer 3.1200
what is the question:
how many kilometers did each player run.
what we know:
we know that the field has the lengtth of 120 meters and the width of 80 meters.
what we did:
We used the pythagorean theorem. we divided 120 by 2 we got the answer 60 we divided
since they only went half way up. so what we did is this:
60^2+80^2=diag.
so 60 ^2 = 3600 and 80 ^2 =6400 next we added them both.3600+6400=10,000. next
we wanted to find the square root of 10,000 we got 100. for every time they went
diagonaly it was 100 meters.every time they went up or down it was 80 meters. so they
went :
they went up 100 meters diagonaly,
they went down 100 meters diagonaly
they went straight up 80 meters
they went back down 100 meters diagonaly
then they went back up 100 meters diagonaly
then they went down 80 meters again.
in total they went 560 meters. since they went around three times we multiplied it by 3
which we got the answer of 1,680.
since we know that 1,000 meters equal 1 kilometer we divided. 1,680 divided by 1,000
equals 1.68 kilometers we rounded the answer to 2 kilomters.
Our answer:
we rounded it to 2 kilometers.
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Page 5 of 14
Student 24
Each player will run
0.432 kilometers three
times around the
Double V.
Student 25
the pattern is that
their running a V every
other time then
finishing at the center
to the opposite to
where they started
Each player will run
1.68 kilometers.
Student 26
Student 27
Each player will run
1.68 kilometers.
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First you have to know the equation you are useing. I used the Pythagirean theorem- A
square+ B square + c square. So then I looked at the information I had and i can up wit
120 to the secound power + 80 to the seound power = c square. Then i multiply 12 times
12 and got 14400. Then 80 times 80 and it equaled 6400. i added them up and i got
20800= C square. Then i found the Square route of 20800 and I got 144.2. I rounded it
off to 144. So now I have c square =144. I Mulitplied 144 times 3 because 3 is how many
times one player ran around the Double V. And I got 432. So the I divided it to 1000
because 1000= 1 kilometer. And I got 0.432. So my answer is 432 kilometers for each
player running 3 times around the Double V.
a2+b2=c2
120+80=c2
240+160=c2
400=c2
c2=800
First I saw that the field was divided into two to form two
congruent right triangles. I also saw that the first path travelled
along the hypotenuse of that trinagle. So I used the Pythagorean
Theoreum to find its length; doing this would find part of the
distance of the run. 120 / 2 = 60 and using the Pythagorean
Theoreum, 3600 + 8400 = 10000. The square root of this is 100, so
the distance from the southwestern corner to the northern middle
point is 100 m and since the run travelled then down to the
southeastern corner, I added another 100 m because the trinagles are
congruent. I added another 160 m for the times when the path ran
along the width twice. And then there was a repeat of the first
paths, the ones that ran along the hypotenuse, so I added another
200 m for a total of 560 m. I multiplied this by 3 because they
players ran this pattern 3 times; the product came out as 1680 m.
And because there are 1000 m in 1 km, I divided 560 by 1000 to get
1.68 km.
I first drew a diagram of the soccer field entering all
measuremnts (80m on side, 120m on bottom, ect.). I then drew the
path in pen to not get confused on what was the path and what
wasn't. I took the two sides (80m each) and added them together to
get part of the length with 160m. I then needed to find the length
of the hypotenuse of the triangles that were drawn. I did 80m^2 *
60m^2=c^2. I ended up getting 100m=c. So since there were 4 of the
little crisscrosses or hypotenuses I multiplied that by 4 to get
400m. I then added the 400m to the 160m from earlier to get 560m.
Page 6 of 14
Student 28
Each player will run
about 1.8 kilometers.
Student 29
Each player has to run
1.68 kilometers.
Bonus: The team at my
school
Student 30
Each player will run
560 meters per
"double V." So each
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But since they ran it three times I multiplied that by three to get
1680m. But since they were asking for the distance in kilometers I
divided that by 1000 to get 1.68km.
First I took the 2 sides which were each 80 and I added them together
to gat 160 meters. Then because I knew that they ran along the
hypotenuse of a 45-45-90 triangle I used the formula a* the square
root of 2. So I did 80(side length) * square root of 2 and found that
the hypotenuse was about 113 meters long. Because the players run the
triangle 4 times I multiplied 113 by 4. My answer was 452 meters. Then
I added the 160 from before on to that. And then because the players
run it 3 times I multiplied that by 3. I got a total of 1837 meters.
To convert it into kilometers, I divided it by 1000. That is how I got
1.837 kilometers which I rounded to about 1.8 kilometers that each
player runs each pratice during the Double V.
First of all if we look closely at the field it is split into 4 right
triangles. Because we know that the Pythagorean Theorem is a2+ b2= c2,
and that it only works on right triangles we know that we can use the
Pythagorean Theorem for this triangle. If we know that half of the
length of the field is the bottom leg of the triangle we need to
calculate it. So we divide 120 meters by 2 to get 60 meters for the
base. Now we plug in 60 meters for a and 80 meters for b. We should
come up with 3600 meter2 + 6400 meters2= c2. We add 3600 meters2 and
6400 meters2 together and get 10,000 meters2. Now we know that 10,000
meters2 is c2 we need to find the square root of it. The square root
of 10,000 meter2 is 100 meters. So 100 meters is the hypotenuse or the
diagonal run. Then we multiply it by 4 because there are 4 diagonal
runs and we add the two 80 meter runs on the sides to get 560 meters
per a double-V run. Since each player runs this 3 times, so we
multiply 560 meters by 3 to get 1680 meters. To convert it to
kilometers, we divide this by 1000 to get 1.68 kilometers.
Bonus: To calculate rectangular field perimeter we have 75 yards + 75
yards + 115 yards + 115 yards and get 380 yards for one lap. Now we
have to multiply it by 5 because there are 5 laps and get 1900 yards.
(Note: 1yd = 0.9144m & 1m= 1.0936yd) To convert it to meters we
multiply 1900 yards by 0.9144. We get about 1737m for the 5 laps. So
the 5 laps have more of a distance.
What: What I did was first I used the Pathagorean Thereom to
clculate the hypotenuse per half feild. Half of a "V" is 100 meters
long. This meant that every "double V" is 200 meters long. I then
Page 7 of 14
student runs about
1680 meters which is
1.68 of a kilometer.
added the rest of the sides together and got 560 meters for
every "double V." I took that "double V" an mutiplied it by three
because that is how many times each player runs the "double V."
Lastly, I got 1680 meters and converted that to kilometers and got
1.68 kilometers.
Why: I did it this way because I knew once I had the hypotenuse of
half the diagnal it would be easy from there. The hypotenuse is 100
meters long and since it's a "V" I needed to double it. Then, I
added the rest of the sides to that value. Each "double V" is about
560 meters long. lastly I mutiplied the "double V" by three because
the players run it three times. Each player runs 1680 meters which
is about 1.68 kilometers.
Student 31
The players run 1.68
km in 3 double-v laps.
Steps: 1. I found the length of the hypotenuse by using the
pathagoreen thereom. Each side is 100 meters.
2. I doubled that to get the whole length of the "V." 200
meters.
3. I added the rest of the lengths of the sides to
the "double V." 560 meters.
4. With the 560 meters per "double V" I mutiplied it by three
which is how many times the player has to run it. That was 1680
meters long.
5. I then converted that to kilometers which is 1.68
kilometers.
First I used tha pythagorean thereom of a^2 + b^2 = c^2> I
substituted in a and b as 60 meters^2 + 80 meters^2 = c^2. After
solving that I got 10,000 meters = c^2.C equals the square root of
10,000 so c = 100 meters.
The v's equal 200 meters and the sides are 80 meters.When you add
them up you get 1 lap as 560 meters. When you multiply that lap by 3
you get 1,680 meters as three laps. Since 1,000 meters equal 1
kilometer, I divided 1,680 meters by 1000 meters to get 1.68
kilometers as three laps
Student 32
The soccer team
should run 2.24
kilometers each day.
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To start out my POW, I calculated the hypotenuse of the squares, or
halves of the court. To do this, I performed the operation of 80
meters squared + 60 meters squared (because half of the court length
Page 8 of 14
Student 33
each player ran 800
meters.
Student 34
The answer to the
problem of the week is
1680 meters, or 1.68
kilometers. The
answer to the extra
credit is that the team
that ran the Double Vs
and they ran 1378.1
more meters.
© 1994-2016 Drexel University
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is 60) = c squared.
80^2+60^2 = C^2
I then multiplied each of these numbers out to further complete the
problem.
(80*80)= 6400 + 3600 = (60*60) = C^2
I then added these two numbers together so I could solve for C.
6400 + 3600 = 10,000 or c^2
To find out the square root of 10,000, I plugged the number into my
calculator and solved.
10,000 square rooted = 100 meters
To find the total distance of the double V pattern, I added together
the four hypotenuses and two side lengths together.
(100*4) + (80*2) = 400 + 160 or 560 meters.
Because the team runs 3 of these patterns, I multiplied this by 3.
560 meters * 3 = 1,680 meters.
The problem said that I should answer in kilometers, so I converted
1,680 meters into 1.68 kilometers.
i first found out that it wasn't a square because it was 80by60 for
each rectangle. then i realized where the lines intersected for each
recatangle was the center. from number 5 to 4 was 160 meters because
if the side length was 80 then because the recatangle divided by 2 is
a right triangle and the hypotnuse is 2 * the smaller length. so 80 *
2 = 160. so then if the left side is congruent to the right side then
it would be 6 to 5 is 80, 5 to 4 is 160 4 to 3 is 160 3 to 2 iis 80,
2 to 1 is 160 and 1 to 6 is 160 so the equation is 80 + 160 +160 + 80
+ 160 +160 = 800.
The way that I solved this problem is by first finding out the length
of the diagnal. To find this, I used the pythagorean theorem which is
a^2+b^2=c^2. I plugged in the numbers and got that c^2=10,000. I took
the square root of that and got 100 meters. I took all of the lengths
that were ran and got 560. It says that they ran the Double V three
times, so I times the 560 by 3 to get 1680 meters. I divided that by
1,000 to get 1.68 kilometers.
Extra Credit:
I took the 75, I added a another 75, plus 2 115s to get the perimeter
that they ran. I got 380. I times that by 5 because they ran 5 laps
and got 1900. I then had to convert that into inches by timesing 1900
by 36 because there are 36 inches in a yard. I then had to convert
that into meters by dividing that by 39 because there are 39 inches
in a meter. I got 292.3. I subracted 292.3 meters from 1680, and got
Page 9 of 14
Student 35
They have to run .56
kilometers.
Student 36
Each soccer player
runs about 1.68
kilometers during each
practice session.
Student 37
Each player runs
1.8376 kilometers.
Student 38
Each player runs 1.2
kilometers.
Student 39
Each person ran 400
meters.
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1378.1 meters.
I found all the sides of one of the triangles by using the
pathagorian therumand i knew that all of the triangles are congruent.
Why I did what I did is because the triangles were right
triangles and I knew both legs of the triangle.
First, I knew that 1/4 of the soccer field was a triangle, 60 on one
leg, 80 on the other. To find out the hypotenuse, I had to use the
formula a^2+b^2=c^2, so my problem looked like
this:(60*60)+(80*80)=c*c. 60*60=3600 and 80*80=6400. Those two numbers
added together equaled 10000. The square root of that was 100, which
is the hypotenuse. There are 4 "hypotenuses" in the soccer field in
which the players ran in, so I multiplied 100 by 4. That equaled 400.
Next, I added to that 160, because the players also ran two other
sides that were both 80 meters and got 560 meters. Since the soccer
players ran 3 of the double "V" pattern, I multiplied 560 by 3 and got
1680 meters. The problem says to put your answer in kilometers, and
since there are 1000 meters in one kilometer, I divided 1680 by 1000
and got my answer, 1.68 kilometers.
I figured that if the two 80 lengths were the hypontenous of a right
triangle, than if you divided it by the square root of two, you would
get 56.56 m. on every other side since the whole thing was symetrical.
so I had 8 sides with lengths of 56.56 m(or 56.56*8) and 2 sides with
lenghts of 80 m (or 80 *2) so I did the problem (80*20) + (56.56*8)and
I got 1837.6 meters. then, to convert it to kilometers, I divided it
by 1000 and got 1.837 kilometers.
First, I had to divide the 2 triangles. I knew that one side was 120
m. and the other sides were the same, so I set it up like x + x =
120. x= 60. Then I noticed 2 Vs, which has four sides. I did 60 * 4
= 240. Then I noticed two sides to turn, which is 80 m., I did 80 *
2 = 160. Then I did 160 + 240 = 400, because I knew that if I add
this up together, I would have the total of one lap. But, I noticed
that he asked for 3 laps, which I could do 3 * 400 = 1200 m. Then he
asked for kilometers, so I moved the decimal point three times to
the left, which I got 1.2 km.
To find the answer to this POW I needed to find some lengths. First
I used the foumula for a parrlelagram to find the area of the
rectangle. To do this I multiplied 120meters by 80meters. Then I
divided the area by two to find the smaller rectangle in it. Then i
divided the quotient by four to find the area of the triangle. Then
by dividing the width by half I. Then i divided each triangle by
Page 10 of 14
Student 40
Each player runs 1.68
kilometers while
running this Double V
pattern 3 times.
Student 41
A person runs 612.56
meters in the double v
run.
Student 42
They must run 5.6 KM
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making a line from the top to the bottom making a right angle. Then
using the 30 60 90 formula i found the lengths i needed. Since the
line are congruent i just muliplied the line by how many diangle
lines. Then i added that to both of the sides with 80 meters to get
my answer.
the length of the field is 120 meters, and the width of the field was
80 meters.
half of one V can be pictured as the hypotenuse of a right triangle.
half of the field's length is 60 ( 120 / 2 ) and the width is the
kept same.
using the pythagorean theorum, a(a) + b(b) = c(c) you can find the
lenth of the hypotenuse. 60(60) + 80 (80) = c(c)
3600 + 6400 = c(c)
10000 = c(c) = c(squared)
(the square root of) 10000 = the square root of c(squared)
100 meters is c = c is 100
since there are two halves of the V to make a complete V, multiply
the length of the hypotenuse of the right triangle by two.
100 x 2 = 200 meters
since there are two V's to be run, multiply 200 by 2 = 400 meters
since the runners must also run th width of the field twice, multiply
the length of the width of the field by 2 ( 80 m x 2 = 160 meters ).
then add the length of the two V's and the length of the width(2).
400 + 160 = 560 meters ran.
there are 1,000 meters in a kilometer so
560 meters is equal to 0.56 kilometers.
since each player runs this double V pattern 3 times, multiply
0.56 kilometers by 3. ==> 0.56 km x 3 = 1.68 kilometers
To find the answere I needed to find the length of one v so i can
double it and find the total of both the v's and i all ready know
the rest lenghts.to find the length of v you divide it by half and
now in one half of the rectangle you have a right angle.to find that
length you need to take one of the smaller length and time it by The
squre root of 2.and you get the ansewerand times by four and add 160
and get the answere.
To solve this POW you can use many formulas, such as the tangent sine
and cosine, but I chose the Pythagorean theorem. What I did was
divided the rectangle into two squares, then I divided the two
squares into two triangles so it looked like this…(the drawing stayed
on word)
Page 11 of 14
Student 43
Each player ran 1.68
kilometers.
Student 44
Each player runs 1.68
kilometers.
Student 45
1.680km
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In order to find the “red lines” [the hypotenuse] you can use the
Pythagorean theorem the hypotenuse is 100m, since there are four
hypotenuses I multiplied 100 by 4 to get 400m but there also 2 times
when the players must run straight on “the legs” and that means you
must add another 160 so the total is 560m, or 5.6 km…Each person must
run 5.6 km.
Bonus: Your team runs the perimeter (380 m) 5 times, the other runs
the double V 3 times. You run a total of 1900 m and the other school
runs a total of 1680 m. Your school runs more.
First, I used the formula a^2 + b^2 = c^2 to find out that the
diagonal of half the field is 100 meters. Then I added together all
the measurements (100+10+100+100+80+80) to get 560. Then I
multiplied that by three because the Double V was ran three times. I
got 1,680. Then. because the answer had to be in kilometers and
because a kilometer is 1,000 meters, I divided 1,680 by 1,000. My
final answer was 1.68 kilometers.
First, I found out what the length of half the field was, which came
out to be 60. I did this so I could add it into the hypotenhuse
formula. Next, I added the information into the hypotenhuse formula.
I did this to find the hypotenhuse which came out to be 100. Siince
there were 400 diagonal lines and 1 down line, I added
100+100+100+100+80+80. I did this to find the distance of one lap
which was 560 merters. I multiplied that by three. I did this
because each player has to run around the course three times. After
coming up with 16080 meters I converted it to kilometers and got
1.68 kilometers.
This question has to ways of finding the answer. The first way is
the most noticeable one. This way you look at a corner and you will
see a big triangle. (I used the triangle 423.) When you see this
triangle you notice that it has a right angle, this means you could
use the Pythagorean Theorem to find out one edge of it (or in other
words half of one V.) To use the formula you need to know 2 of the
sides, and you already know one and that is the 80 meters. The other
side that you use is the perimeter of the rectangle; to find this
one you divide 120 by 2 because it goes to the center line. This
gives you 60. Now because we are using the Pythagorean Theorem we
need to square 80 and 60 and then add them up which you would get
10000. Because this equals C sq you need to find the square root of
it which is 100. So 100 is half of a V and because there is 2 V’s
you multiply 100 by 4 to get 400. Now because they also run the 80m
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Student 46
Each player runs 1.68
kilometers if they do
the "double V" 3
times.My explanation
is as follows.
on both sides you need to multiply 80 by 2 and then add it to 400
and then you would get 560. Then because they run the lap 3 times
you multiply that by 3 to get 1680m so to get one kilometer (1000
meters) you would divide by 1000 to get 1.680km.
Another way to do this (which isn’t that obvious) is to look
at any of triangles on the edges right or left side (I used the one
on the right edge), at first you see that I doesn’t have a right
angle, but if you cut it in half and then you would have a right
angle. Now because one of it’s corners start midway between 80
meters you use 40 and because when you divided it in half you made a
line that goes ¼ the way across the field so 120/4=30, so you have
30sq and 40sq because of the Pythagorean Theorem which adds up to
2500. Now because that equals C sq and I want C, so I need to find
the sq root of C sq which is 50 so the other edge of that triangle
is 59. Now because there are 8 of those little lines you do 50 times
8 which equals 400, then because you run an extra 80 meters twice
you add 160 to it getting 560. Then because they ran 3 laps it is
multiplied by 3 which is 1680, then because it is in kilometers you
divide by 1000 getting 1.680.
I knew the length of the soccer field is 120 meters and the width of the soccer field is 80 meters, so to find the length of
the diagonal line I had to cut the 120 in half because the end of the diagonal line is at the center. So my 2 dimensions
are 60 and 80 for the shape of the right triangle on one of the sides of the diagonal line. If you add the square of the
first leg of the right triangle which, in this case is 60 meters, and the square number of the second leg you would come
up with the area of the square off the hypotenuse, which ,in this case, equals 10,000.So I had to find the square root of
10,000, and that would give me the length of the hypotenuse. I knew that the square root of 10,000 would have to be
more than 80 because that is the length of the longest leg and the hypotenuse is longer than both of the legs, so I tried
100. So I did 100 times 100 and got 10,000 so the length of the hypotenuse is 100 meters. So if one of the diagonal
lines is 100 meters and all of the diagonal lines are equal, then that means all of the other diagonal lines are 100 meters
long. So I added up all 4 diagonal lines and got 400. But I still have to add the two 80s to the 400, so I added them and
got 560 meters. Then it said that the players had to run the double V three times so I multiplied 560 by three and I got
1680 meters. But I still have to find the number of the kilometers that the players ran, and I knew that there are 1,000
meters in one kilometer, so I have one full kilometer. But I still have the left over 680 meters so I know that if I had 500
meters left I would have .5 kilometers, so for this I have .68 kilometers and so the full amount of kilometers that the
players ran is 1.68.
Student 47
Student 48
Each player ran 1.68
kilometers.
© 1994-2016 Drexel University
http://mathforum.org/pows/
I looked part of this problem up on the internet. I looked on google and found a formula:a squared+b squared =c
squared. The hypotenuse(the long side) is c squared, which is what I was trying to find. I already knew that a equaled
80 meters, and b equaled 60 meters. That means I'm doing (80x80)+(60x60). 80x80=6,400, and 60x60=3,600. Now I'm
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Student 49
My answer is 1.68
kilometer.
doing 6,400+3,600, which equals 10,000. This number is c squared. I had to find the square root of 10,000, which is 100.
Now I have the plain line of c. This soccer field has 2 sides that equal 80 meters, so I know that each player runs at least
that much. They all run the "Double V" 3 times, so that means I'm now doing 160x3. That gave me 480. Next, in each
lap around the "Double V", they run the 100 meter stretch 4 times, so I know that they each run at least 400 meters.
Again, they each run the "Double V" 3 times, so I now need to do 400x3. Now I have 1,200. Finally, I need to add 480
and 1,200. That got me to 1,680. As my final few steps, I can take off the zero and put in a decimal point. My sure
answer is 1.68 kilometers run by each player.
I got my anwer by doing algebra. First I had to find the length of each leg of a right triangle. The length of the verticle
leg is 80 meters because the triangle length is the same as the height of the rectangle which is 80 meters. Next I had to
find the horizontal leg which is 60 meters because the whole length of the rectangle is 120 meters and the leg is half of
the 120 meters which is 60 meters.The rule is A squared + B squared = C squared. A is 80 meters so you have to square
it 80x80=6,400. Next you have to do B squared which is 60x60=3,600. So now you have to add 6,400+3,600=10,000 ,
next I have to find the square root of 10,000 because C squared is the same as C(C), and I need to know what one
C equals. 100x100=10,000, C=100. So I figured out the length of C, which is the length of all the diagonals. The length
of the circuit is 560 meters. So if they have to do three laps that equals 560x3=1,680 meters. If there are 1,680 thats
one kilometer and 680 is basically is .68 so the answer is 1.68 kilometers.
Student 50
© 1994-2009 Drexel University
http://mathforum.org/pows/
© 1994-2016 Drexel University
http://mathforum.org/pows/
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