Pythagorean Theorem

1) A right triangle has a hypotenuse of 15 m and one leg of 8 m. Find the other leg (round to the nearest tenth).

11.9 m

12.7 m

12.5 m

13.1 m

With hypotenuse 15 and one leg 8, the other leg is about 12.7 m.

Explanation

With hypotenuse 15 and one leg 8, the other leg is about 12.7 m.

2) A right triangle has legs of 11 cm and 60 cm. Find the hypotenuse.

60.9 cm

61 cm

62 cm

59 cm

Legs 11 and 60 give a hypotenuse of 61 cm.

Explanation

Legs 11 and 60 give a hypotenuse of 61 cm.

3) A right triangle has a hypotenuse of 85 cm and one leg of 36 cm. What is the other leg?

80 cm

75 cm

77 cm

78 cm

With hypotenuse 85 and one leg 36, the other leg is 77 cm.

Explanation

With hypotenuse 85 and one leg 36, the other leg is 77 cm.

4) A right triangle has a hypotenuse of 65 cm and one leg of 63 cm. What is the other leg?

10 cm

12 cm

14 cm

16 cm

With hypotenuse 65 and one leg 63, the other leg is 16 cm.

Explanation

With hypotenuse 65 and one leg 63, the other leg is 16 cm.

5) A right triangle has legs 6 cm and 8 cm. What is the hypotenuse?

9 cm

14 cm

10 cm

11 cm

To find the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, a = 6 cm and b = 8 cm. Therefore, c² = 6² + 8² = 36 + 64 = 100. Taking the square root gives c = √100 = 10 cm.

Explanation

To find the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, a = 6 cm and b = 8 cm. Therefore, c² = 6² + 8² = 36 + 64 = 100. Taking the square root gives c = √100 = 10 cm.

6) A right triangle has legs 5 m and 12 m. What is the hypotenuse?

11 m

12 m

13 m

14 m

To find the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that a² + b² = c², where c is the hypotenuse and a and b are the lengths of the other two sides. Here, a = 5 m and b = 12 m. Therefore, the calculation is: 5² + 12² = 25 + 144 = 169. Taking the square root of 169 gives us c = 13 m. Hence, the hypotenuse is 13 m.

Explanation

To find the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that a² + b² = c², where c is the hypotenuse and a and b are the lengths of the other two sides. Here, a = 5 m and b = 12 m. Therefore, the calculation is: 5² + 12² = 25 + 144 = 169. Taking the square root of 169 gives us c = 13 m. Hence, the hypotenuse is 13 m.

7) A right triangle has a hypotenuse of 29 cm and one leg of 12 cm. What is the other leg (round to the nearest tenth)?

24:5 cm

24:9 cm

25:8 cm

26:4 cm

To find the length of the other leg in a right triangle, you can use the Pythagorean theorem, which states that a² + b² = c², where c is the hypotenuse. Here, a is 12 cm, and c is 29 cm. Rearranging gives b² = c² - a². Calculating this: b² = 29² - 12² = 841 - 144 = 697. Thus, b = √697, which is approximately 26.4 cm when rounded to the nearest tenth.

Explanation

To find the length of the other leg in a right triangle, you can use the Pythagorean theorem, which states that a² + b² = c², where c is the hypotenuse. Here, a is 12 cm, and c is 29 cm. Rearranging gives b² = c² - a². Calculating this: b² = 29² - 12² = 841 - 144 = 697. Thus, b = √697, which is approximately 26.4 cm when rounded to the nearest tenth.

8) A right triangle has a hypotenuse of 17 cm and one leg of 15 cm. What is the other leg?

8 cm

9 cm

10 cm

11 cm

Subtract the square of 15 from the square of 17 and take the root; that’s 8 cm.

Explanation

Subtract the square of 15 from the square of 17 and take the root; that’s 8 cm.

9) Find the hypotenuse of a right triangle with legs 9 ft and 40 ft.

41 ft

38 ft

42 ft

45 ft

Legs 9 and 40 make the well-known 9–40–41 triangle; the hypotenuse is 41 ft.

Explanation

Legs 9 and 40 make the well-known 9–40–41 triangle; the hypotenuse is 41 ft.

10) A right triangle has a hypotenuse of 10 m and one leg of 6 m. Find the other leg (round to the nearest tenth).

5.2 m

6.7 m

7.8 m

8.0 m

With hypotenuse 10 and one leg 6, the other leg works out to 8.0 m.

Explanation

With hypotenuse 10 and one leg 6, the other leg works out to 8.0 m.

11) Find the missing leg of a right triangle if the hypotenuse is 85 cm and one leg is 84 cm (round to the nearest tenth).

9 cm

12 cm

13 cm

15 cm

With hypotenuse 85 and one leg 84, the missing leg is 13 cm.

Explanation

With hypotenuse 85 and one leg 84, the missing leg is 13 cm.

12) A right triangle has legs of 8 m and 15 m. What is the hypotenuse?

16 m

19 m

20 m

17 m

Legs 8 and 15 give a hypotenuse of 17 m.

Explanation

Legs 8 and 15 give a hypotenuse of 17 m.

13) A right triangle has a hypotenuse of 34 cm and one leg of 30 cm. Find the other leg (round to the nearest tenth).

12 cm

16 cm

18 cm

20 cm

With hypotenuse 34 and one leg 30, the other leg is 16 cm.

Explanation

With hypotenuse 34 and one leg 30, the other leg is 16 cm.

14) A right triangle has a hypotenuse of 20 cm and one leg of 5 cm. Find the other leg (round to the nearest tenth).

12 cm

19.4 cm

18 cm

15 cm

With hypotenuse 20 and one leg 5, the other leg is about 19.4 cm.

Explanation

With hypotenuse 20 and one leg 5, the other leg is about 19.4 cm.

15) Find the hypotenuse of a right triangle with legs 7 cm and 24 cm.

25 cm

23 cm

26 cm

28 cm

Legs 7 and 24 give a hypotenuse of 25 cm.

Explanation

Legs 7 and 24 give a hypotenuse of 25 cm.

16) A right triangle has a hypotenuse of 29 ft and one leg of 20 ft. What is the other leg?

15 ft

18 ft

21 ft

22 ft

With hypotenuse 29 and one leg 20, the other leg is 21 ft.

Explanation

With hypotenuse 29 and one leg 20, the other leg is 21 ft.

17) A right triangle has a hypotenuse of 53 in and one leg of 14 in. What is the other leg (round to the nearest tenth)?

48.2in

46.4 in

51.1 in

54.2 in

With hypotenuse 53 and one leg 14, the other leg is about 51.1 in.

Explanation

With hypotenuse 53 and one leg 14, the other leg is about 51.1 in.

18) A right triangle has legs of 9 m and 13 m. What is the hypotenuse (round to the nearest tenth)?

14.2 m

15.8 m

16.5 m

17.1 m

Legs 9 and 13 give a hypotenuse of about 15.8 m.

Explanation

Legs 9 and 13 give a hypotenuse of about 15.8 m.

19) A right triangle has a hypotenuse of 37 cm and one leg of 12 cm. What is the other leg?

35 cm

33 cm

32 cm

31 cm

With hypotenuse 37 and one leg 12, the other leg is 35 cm.

Explanation

With hypotenuse 37 and one leg 12, the other leg is 35 cm.

20) Find the hypotenuse of a right triangle with legs 20 m and 21 m.

28.6 m

27.3 m

29.0 m

30.1 m

Legs 20 and 21 give a hypotenuse of exactly 29.0 m.

Explanation

Legs 20 and 21 give a hypotenuse of exactly 29.0 m.