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MathsAges 13-15

Pythagoras: hypotenuse

Calculate the hypotenuse of a right-angled triangle from two perpendicular side lengths. Review suitability for your learners before teaching.

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Age band:Ages 13-15Ages 16-18

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Worksheet StudioPractice pack · Ages 13-15

Pythagoras: hypotenuse

Take your time. Show your thinking.

  1. 1. A right-angled triangle has perpendicular sides 64 cm and 120 cm. Find its hypotenuse.

    64 cm · 120 cm · Pythagoras: hypotenuse

  2. 2. A right-angled triangle has perpendicular sides 45 cm and 108 cm. Find its hypotenuse.

    45 cm · 108 cm · Pythagoras: hypotenuse

  3. 3. A right-angled triangle has perpendicular sides 8 cm and 15 cm. Find its hypotenuse.

    8 cm · 15 cm · Pythagoras: hypotenuse

  4. 4. A right-angled triangle has perpendicular sides 33 cm and 44 cm. Find its hypotenuse.

    33 cm · 44 cm · Pythagoras: hypotenuse

  5. 5. A right-angled triangle has perpendicular sides 32 cm and 60 cm. Find its hypotenuse.

    32 cm · 60 cm · Pythagoras: hypotenuse

  6. 6. A right-angled triangle has perpendicular sides 21 cm and 28 cm. Find its hypotenuse.

    21 cm · 28 cm · Pythagoras: hypotenuse

  7. 7. A right-angled triangle has perpendicular sides 5 cm and 12 cm. Find its hypotenuse.

    5 cm · 12 cm · Pythagoras: hypotenuse

  8. 8. A right-angled triangle has perpendicular sides 40 cm and 75 cm. Find its hypotenuse.

    40 cm · 75 cm · Pythagoras: hypotenuse

  9. 9. A right-angled triangle has perpendicular sides 24 cm and 45 cm. Find its hypotenuse.

    24 cm · 45 cm · Pythagoras: hypotenuse

  10. 10. A right-angled triangle has perpendicular sides 24 cm and 32 cm. Find its hypotenuse.

    24 cm · 32 cm · Pythagoras: hypotenuse

  11. 11. A right-angled triangle has perpendicular sides 15 cm and 36 cm. Find its hypotenuse.

    15 cm · 36 cm · Pythagoras: hypotenuse

  12. 12. A right-angled triangle has perpendicular sides 56 cm and 105 cm. Find its hypotenuse.

    56 cm · 105 cm · Pythagoras: hypotenuse
12 questions · Seed 104729 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Pythagoras: hypotenuse

Answers and reasoning. Review before teaching.

  1. 1. A right-angled triangle has perpendicular sides 64 cm and 120 cm. Find its hypotenuse.

    136 cm

    c² = 64² + 120² = 18496. Taking the positive square root gives c = 136 cm.

  2. 2. A right-angled triangle has perpendicular sides 45 cm and 108 cm. Find its hypotenuse.

    117 cm

    c² = 45² + 108² = 13689. Taking the positive square root gives c = 117 cm.

  3. 3. A right-angled triangle has perpendicular sides 8 cm and 15 cm. Find its hypotenuse.

    17 cm

    c² = 8² + 15² = 289. Taking the positive square root gives c = 17 cm.

  4. 4. A right-angled triangle has perpendicular sides 33 cm and 44 cm. Find its hypotenuse.

    55 cm

    c² = 33² + 44² = 3025. Taking the positive square root gives c = 55 cm.

  5. 5. A right-angled triangle has perpendicular sides 32 cm and 60 cm. Find its hypotenuse.

    68 cm

    c² = 32² + 60² = 4624. Taking the positive square root gives c = 68 cm.

  6. 6. A right-angled triangle has perpendicular sides 21 cm and 28 cm. Find its hypotenuse.

    35 cm

    c² = 21² + 28² = 1225. Taking the positive square root gives c = 35 cm.

  7. 7. A right-angled triangle has perpendicular sides 5 cm and 12 cm. Find its hypotenuse.

    13 cm

    c² = 5² + 12² = 169. Taking the positive square root gives c = 13 cm.

  8. 8. A right-angled triangle has perpendicular sides 40 cm and 75 cm. Find its hypotenuse.

    85 cm

    c² = 40² + 75² = 7225. Taking the positive square root gives c = 85 cm.

  9. 9. A right-angled triangle has perpendicular sides 24 cm and 45 cm. Find its hypotenuse.

    51 cm

    c² = 24² + 45² = 2601. Taking the positive square root gives c = 51 cm.

  10. 10. A right-angled triangle has perpendicular sides 24 cm and 32 cm. Find its hypotenuse.

    40 cm

    c² = 24² + 32² = 1600. Taking the positive square root gives c = 40 cm.

  11. 11. A right-angled triangle has perpendicular sides 15 cm and 36 cm. Find its hypotenuse.

    39 cm

    c² = 15² + 36² = 1521. Taking the positive square root gives c = 39 cm.

  12. 12. A right-angled triangle has perpendicular sides 56 cm and 105 cm. Find its hypotenuse.

    119 cm

    c² = 56² + 105² = 14161. Taking the positive square root gives c = 119 cm.

12 questions · Seed 104729 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Pythagoras: hypotenuse

Take your time. Show your thinking.

  1. 1. A right-angled triangle has perpendicular sides 64 cm and 120 cm. Find its hypotenuse.

    64 cm · 120 cm · Pythagoras: hypotenuse

  2. 2. A right-angled triangle has perpendicular sides 45 cm and 108 cm. Find its hypotenuse.

    45 cm · 108 cm · Pythagoras: hypotenuse

  3. 3. A right-angled triangle has perpendicular sides 8 cm and 15 cm. Find its hypotenuse.

    8 cm · 15 cm · Pythagoras: hypotenuse

  4. 4. A right-angled triangle has perpendicular sides 33 cm and 44 cm. Find its hypotenuse.

    33 cm · 44 cm · Pythagoras: hypotenuse

  5. 5. A right-angled triangle has perpendicular sides 32 cm and 60 cm. Find its hypotenuse.

    32 cm · 60 cm · Pythagoras: hypotenuse

  6. 6. A right-angled triangle has perpendicular sides 21 cm and 28 cm. Find its hypotenuse.

    21 cm · 28 cm · Pythagoras: hypotenuse

  7. 7. A right-angled triangle has perpendicular sides 5 cm and 12 cm. Find its hypotenuse.

    5 cm · 12 cm · Pythagoras: hypotenuse

  8. 8. A right-angled triangle has perpendicular sides 40 cm and 75 cm. Find its hypotenuse.

    40 cm · 75 cm · Pythagoras: hypotenuse

  9. 9. A right-angled triangle has perpendicular sides 24 cm and 45 cm. Find its hypotenuse.

    24 cm · 45 cm · Pythagoras: hypotenuse

  10. 10. A right-angled triangle has perpendicular sides 24 cm and 32 cm. Find its hypotenuse.

    24 cm · 32 cm · Pythagoras: hypotenuse

  11. 11. A right-angled triangle has perpendicular sides 15 cm and 36 cm. Find its hypotenuse.

    15 cm · 36 cm · Pythagoras: hypotenuse

  12. 12. A right-angled triangle has perpendicular sides 56 cm and 105 cm. Find its hypotenuse.

    56 cm · 105 cm · Pythagoras: hypotenuse
12 questions · Seed 104729 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Pythagoras: hypotenuse

Answers and reasoning. Review before teaching.

  1. 1. A right-angled triangle has perpendicular sides 64 cm and 120 cm. Find its hypotenuse.

    136 cm

    c² = 64² + 120² = 18496. Taking the positive square root gives c = 136 cm.

  2. 2. A right-angled triangle has perpendicular sides 45 cm and 108 cm. Find its hypotenuse.

    117 cm

    c² = 45² + 108² = 13689. Taking the positive square root gives c = 117 cm.

  3. 3. A right-angled triangle has perpendicular sides 8 cm and 15 cm. Find its hypotenuse.

    17 cm

    c² = 8² + 15² = 289. Taking the positive square root gives c = 17 cm.

  4. 4. A right-angled triangle has perpendicular sides 33 cm and 44 cm. Find its hypotenuse.

    55 cm

    c² = 33² + 44² = 3025. Taking the positive square root gives c = 55 cm.

  5. 5. A right-angled triangle has perpendicular sides 32 cm and 60 cm. Find its hypotenuse.

    68 cm

    c² = 32² + 60² = 4624. Taking the positive square root gives c = 68 cm.

  6. 6. A right-angled triangle has perpendicular sides 21 cm and 28 cm. Find its hypotenuse.

    35 cm

    c² = 21² + 28² = 1225. Taking the positive square root gives c = 35 cm.

  7. 7. A right-angled triangle has perpendicular sides 5 cm and 12 cm. Find its hypotenuse.

    13 cm

    c² = 5² + 12² = 169. Taking the positive square root gives c = 13 cm.

  8. 8. A right-angled triangle has perpendicular sides 40 cm and 75 cm. Find its hypotenuse.

    85 cm

    c² = 40² + 75² = 7225. Taking the positive square root gives c = 85 cm.

  9. 9. A right-angled triangle has perpendicular sides 24 cm and 45 cm. Find its hypotenuse.

    51 cm

    c² = 24² + 45² = 2601. Taking the positive square root gives c = 51 cm.

  10. 10. A right-angled triangle has perpendicular sides 24 cm and 32 cm. Find its hypotenuse.

    40 cm

    c² = 24² + 32² = 1600. Taking the positive square root gives c = 40 cm.

  11. 11. A right-angled triangle has perpendicular sides 15 cm and 36 cm. Find its hypotenuse.

    39 cm

    c² = 15² + 36² = 1521. Taking the positive square root gives c = 39 cm.

  12. 12. A right-angled triangle has perpendicular sides 56 cm and 105 cm. Find its hypotenuse.

    119 cm

    c² = 56² + 105² = 14161. Taking the positive square root gives c = 119 cm.

12 questions · Seed 104729 · Age guidance, not curriculum certification