PYTHAGOREAN TRIPLES
(3, 4, 5)
(6, 8, 10) (12, 16, 20)
(5, 12, 13) (10, 24, 26)
(7, 24, 25)
(8, 15, 17)
(9, 40, 41)
(11, 60, 61)
(12, 35, 37)
(20, 21, 29)
# 1.
In a right triangle, if “a” and “b” represent
the lengths of the legs and “c” represents
the length of the hypotenuse, find the
missing side length in each of the
following:
(a.) a = 10, b = 24
______
(b.) a = 9, c = 13
______
(c.) b = 18, c = 30
______
(d.) a = 6, c = 10
______
# 2.
5
12
x
Find the value of x
using the
Pythagorean
Theorem.
x = ______
# 3.
10
Find the value of x using the
Pythagorean Theorem.
x = ______
# 4.
3
x = ______
Find the
value of x
using the
Pythagorean
Theorem.
# 5.
Find the value of x
using the Pythagorean
Theorem.
5
x
x = ______
# 6.
x
Find the value
of x using the
Pythagorean
Theorem.
x = ______
16
# 7.
56
65
Find the value
of x using the
Pythagorean
Theorem.
x
x = ______
# 8.
To get from point A to point B you must avoid
walking through a pond. To avoid the pond, you
must walk 34 meters south and 41 meters east.
To the nearest meter, how many meters would
be saved if it were possible to walk through the
pond?
(A.) 22
(B.) 34
(C.) 53
(D.) 75
# 9.
A baseball diamond is a square with sides of 90
feet. What is the shorter distance, to the
nearest tenth of a foot, between first and third
base?
(A.) 90.0 (B.) 127.3
(C.) 180.0
(D.) 180.7
# 10.
A suitcase measures 24 inches long and 18
inches high. What is the diagonal length of the
suitcase to the nearest tenth of a foot?
(A.) 2.5
(B.) 2.9
(C.) 26.5
(D.) 30.0
# 11.
In a computer catalog, a computer monitor is
listed as being 19 inches. This distance is the
diagonal distance across the screen. If the
screen measures 10 inches in height, what is
the actual width of the screen to the nearest
inch?
(A.) 10
(B.) 14
(C.) 16
(D.) 19
# 12.
The older floppy diskettes measured 5 ¼ inches
on each side. What was the diagonal length of
the diskette to the nearest tenth of an inch?
(A.) 5.3
(B.) 6.5
(C.) 7.4
(D.) 7.6
# 13.
Ms. Green tells you that a right triangle has a
hypotenuse of 13 and a leg of 5. She asks you
to find the other leg of the triangle without using
a paper and pencil. What is your answer?
(A.) 5
(B.) 8
(C.) 10
(D.) 12
# 14.
Two joggers run 8 miles north and then 5 miles
west. What is the shortest distance, to the
nearest tenth of a mile, they must travel to
return to their starting point?
(A.) 8.4
(B.) 9.5
(C.) 9.4
(D.) 13.1
# 15.
(A.) 6
(B.) 8
(C.) 10
(D.) 12
# 16.
Oscar’s dog house is
shaped like a tent. The
slanted sides are both 5
feet long and the bottom
of the house is 6 feet
across. What is the
height of the dog house,
in feet, at its tallest
point?
(A.) 3
(B.) 4
(C.) 4.5
(D.) 5
# 17.
Seth made a small
rectangular table for his
workroom. The sides of the
table are 36” and 18”. If the
diagonal of the table
measures 43”, is the table a
square? A table which is
“square” has right angles at
the corners.
(A.) Yes
(B.) No
# 18.
Tanya runs diagonally
across a rectangular field
that has a length of 40
yards and a width of 30
yards, as shown in the
diagram.
What is the length of the
diagonal in yards?
(A.) 50
(B.) 60
(C.) 70
(D.) 80
# 19.
In a right triangle, the shorter leg is 7
units less than the longer leg. The
hypotenuse is 1 unit more than the longer
leg. Find the length of the shorter leg.
# 20.
In a right triangle, the shorter leg is 5 and
the hypotenuse is one unit more than the
longer leg. Find the length of the
hypotenuse.
# 21.
The hypotenuse of a right triangle is 1
more than twice the length of the shorter
leg. The longer leg is 15. Find the
hypotenuse.
# 22.
The foot of a ladder is 10 feet from a wall.
The ladder is 2 feet longer than the height
it reaches on the wall. What is the length
of the ladder?
# 23.
Town A is 65 km due north of Town B.
Town C is 44 km due east of town B. Find
the distance from Town A to Town C.
# 24.
How far from the base of a house do you
need to place a 15-foot ladder so that it
exactly reaches the top of a 12-foot wall?
# 25.
John leaves school to go home. He walks
6 blocks North and then 8 blocks West.
How far is John from the school?
# 26.
Which could be the lengths of the
sides of a right triangle?
(a.) 8, 15, 17
______
(b.) 7, 25, 26
______
(c.) 9, 12, 15
______
(d.) 24, 45, 51
______