Factoring and Ratio, Proportion, Application of
And Geometric
Solving
Proportions
Mean
Proportionality
Theorems
Triangle
Similarity
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Factor:
2
6x
($100 )
– 7x – 5
(2x + 1)(3x – 5)
($100)
Solve and find the
roots.
2
7x
(200)
– 57x + 8 = 0
Answer
X = 1/7 or 8
(200)
State the coordinates
(x, y) for the
equation.
0=
(300)
2
36x
-9
(1/2, 0) and (-1/2, 0)
(300)
Multiply and
Simplify:
(4x – 2)(5x + 3)
(400)
Answer:
2
20x
(400)
+ 2x – 6
Multiply and Simplify:
(x – 2)(x + 3)(x + 4)
(500)
Answer:
3
x
(500)
+
2
5x
– 2x – 24
The area of a rectangle is
2
720 in . If the ratio of the
length to width is 5:4, find
the perimeter of the
rectangle.
(100)
Answer:
108 in.
(100)
(200)
AC = 1562
(200)
The geometric mean of the
quantities
(x + 1) and (x – 6) is (x – 2).
Find the value of x.
(300)
X = -10
(300)
The ratio of the perimeters of
two triangles is 4/7.
What is the ratio of the
triangles’ areas?
(400)
Area ratio is 16/49.
(400)
In the U.S., 4634 million lbs. of
apples were consumed in 2002.
The population of the U.S. that
year was 290 million.
What was the per capita
consumption?
(500)
About 16 lbs. per person
(500)
(100)
Scale factor: 1/3
x:18
y:12
(100)
The lengths of the legs of
right ∆ ABC are 3 ft and 4 ft.
The shortest side of ∆UVW
is 4.5 ft and ∆UVW~∆ABC.
How long is the hypotenuse
of ∆UVW?
(200)
7.5 ft
(200)
(300)
12 and 108
(300)
(400)
12
(400)
Two similar posters have a
scale factor of 4:5. The large
poster’s perimeter is 85
inches. Find the small
poster’s perimeter AND the
ratio of their areas.
(500)
Small perimeter = 68 in
Area ratio = 16/25
(500)
2
in
(100)
24
(100)
(200)
78
(200)
Find x and y
(300)
X=3
Y = 8.4
(300)
Find the value of x.
(400)
X = 4.5
(400)
Find length of 4 segments:
AG, FC, ED and AE
(500)
AG = 2 2/3
FC = 7.5
ED = 11.25
AE = 10
(500)
Are the triangles similar and
EXPLAIN how you know.
(100)
The vertical angles are
congruent. By third angle
rd
Theorem, 3 angles are
congruent. So ∆s are similar.
(100)
Find the value of x and y.
(200)
X = 3 1/3
Y = 4 2/3
(200)
(300)
900,000 km
(300)
Round to
100th place
(400)
KM = 13.33 in
MN = 6.67 in.
LM = 8.67 in.
MP = 4.33 in
(400)
(500)
10 inches
(500)
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