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Grade 8 · Math

Find a right-triangle hypotenuse

Apply the Pythagorean theorem to perpendicular side lengths.

8 generated examples + worked example

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Worked example

A right triangle has legs 6 cm and 8 cm. Find its hypotenuse.

Answer & why

Answer: 10

62 + 82 = 100, and the positive square root of 100 is 10.

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Try these examples

8 reproducible examples from this math generator. Choose New examples for another set.

Question 1

A right triangle has perpendicular legs 32 cm and 60 cm. What is the hypotenuse length in centimeters?

  1. 68
  2. 69
  3. 71
  4. 67
A hint

Use a2 + b2 = c2; c is opposite the right angle.

Answer & why

Answer: 68

322 + 602 = 4624 = 682, so the hypotenuse is 68 cm.

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Question 2

A right triangle has perpendicular legs 10 cm and 24 cm. What is the hypotenuse length in centimeters?

  1. 26
  2. 30
  3. 24
  4. 25
A hint

Use a2 + b2 = c2; c is opposite the right angle.

Answer & why

Answer: 26

102 + 242 = 676 = 262, so the hypotenuse is 26 cm.

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Question 3

A right triangle has perpendicular legs 15 cm and 36 cm. What is the hypotenuse length in centimeters?

  1. 38
  2. 40
  3. 39
  4. 41
A hint

Use a2 + b2 = c2; c is opposite the right angle.

Answer & why

Answer: 39

152 + 362 = 1521 = 392, so the hypotenuse is 39 cm.

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Question 4

A right triangle has perpendicular legs 8 cm and 15 cm. What is the hypotenuse length in centimeters?

  1. 16
  2. 20
  3. 17
  4. 21
A hint

Use a2 + b2 = c2; c is opposite the right angle.

Answer & why

Answer: 17

82 + 152 = 289 = 172, so the hypotenuse is 17 cm.

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Question 5

A right triangle has perpendicular legs 6 cm and 8 cm. What is the hypotenuse length in centimeters?

  1. 11
  2. 8
  3. 14
  4. 10
A hint

Use a2 + b2 = c2; c is opposite the right angle.

Answer & why

Answer: 10

62 + 82 = 100 = 102, so the hypotenuse is 10 cm.

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Question 6

A right triangle has perpendicular legs 3 cm and 4 cm. What is the hypotenuse length in centimeters?

  1. 6
  2. 4
  3. 9
  4. 5
A hint

Use a2 + b2 = c2; c is opposite the right angle.

Answer & why

Answer: 5

32 + 42 = 25 = 52, so the hypotenuse is 5 cm.

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Question 7

A right triangle has perpendicular legs 21 cm and 72 cm. What is the hypotenuse length in centimeters?

  1. 73
  2. 76
  3. 74
  4. 75
A hint

Use a2 + b2 = c2; c is opposite the right angle.

Answer & why

Answer: 75

212 + 722 = 5625 = 752, so the hypotenuse is 75 cm.

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Question 8

A right triangle has perpendicular legs 5 cm and 12 cm. What is the hypotenuse length in centimeters?

  1. 11
  2. 13
  3. 14
  4. 16
A hint

Use a2 + b2 = c2; c is opposite the right angle.

Answer & why

Answer: 13

52 + 122 = 169 = 132, so the hypotenuse is 13 cm.

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