(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)

PYTHAGOREAN TRIPLES

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______

# 1.

a2 + b2 = c2

22 bac

22 2410 c

576100c676c

c = 26

c2 – b2= a2

22 bca

22 913 a

81169 a

88a

a = 9.38

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:(c.) b = 18, c = 30

______

(d.) a = 6, c = 10______

# 1.

c2 – b2= a2

22 1830 a

324900 a576a

a = 24

c2 – a2= b2

22 610 b

36100 b 64b

b = 8

12

5

x

Find the value of x using the Pythagorean

Theorem.

x = ______

# 2.

x2 = 52 + 122

22 125 x

14425x169x

13

8 x

10Find the value of x using the

Pythagorean Theorem.x = ______

# 3.

x2 = 102 – 82

64100 x

36x

6

5

x

3

Find the value of x using the Pythagore

an Theorem.x = ______

# 4.

x2 = 52 – 32

925 x

16x

4

13

x

5

Find the value of x using the

Pythagorean Theorem.

x = ______

# 5.

x2 = 132 – 52

25169 x144x

12

63

x

16

Find the value of x using the

Pythagorean Theorem.

x = ______

# 6.

x2 = 162 + 632

3969256x

4225x

65

56

x65

Find the value of x using the

Pythagorean Theorem.

x = ______

# 7.

x2 = 652 – 562

31364225 x

1089x

33

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

# 8.AB2 = 342 + 412 22 4134 AB16811156 AB

2837ABAB = 53.3 (34 + 41) – 53.3 75 – 53.3 = 21.7

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

# 9.90

ft. 90 ft.

90 ft

.90 ft.

dd2 = 902 + 902

22 9090 d

81008100d

16200dd = 127.3 ft.

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

# 10.

24 in.

18 in.

d

d2 = 182 + 242

22 2418 d576324d

900d d = 30 ft.

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

# 11.

19 in

.10 in.

x

x2 = 192 – 102

22 1019 x

100361 x

261x x = 16.16

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

# 12.

5.25 5.25d

d2 = 5.252 + 5.252

22 25.525.5 d

56.2756.27 d

125.55d d = 7.42

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

# 13.

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

# 14.

8 mi.

5 mi.

d

d2 = 52 + 82

22 85 d

6425d89d

d = 9.4

(A.) 6 (B.) 8 (C.) 10 (D.) 12

# 15.

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

# 16.

3

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

# 17.

362 + 182 =1296 + 324 =

1620

432 = 1849

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

# 18.

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.

# 19.

x = longer legx – 7 = shorter legx + 1 = hypotenuse

125

13

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.

# 20.

x = longer leg5 = shorter leg

x + 1 = hypotenuse

12

13

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.

# 21.

15 = longer legx = shorter leg

2 x + 1 = hypotenuse

8

17

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?

# 22.

10

h

h + 2

24

26

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.

# 23.

B

A

65

C44

AC2 =652 + 442

22 4465 AC

19364225AC

6161AC

AC = 79.5 km

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?

# 24.

15

12

x 9

John leaves school to go home. He walks 6 blocks North and then 8

blocks West. How far is John from the school?

# 25.

6

8

10

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 ______

# 26.

YESNOYESYES