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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 15 cm and 20 cm. Find its hypotenuse.

    15 cm · 20 cm · Pythagoras: hypotenuse

  2. 2. A right-angled triangle has perpendicular sides 30 cm and 40 cm. Find its hypotenuse.

    30 cm · 40 cm · Pythagoras: hypotenuse

  3. 3. A right-angled triangle has perpendicular sides 55 cm and 132 cm. Find its hypotenuse.

    55 cm · 132 cm · Pythagoras: hypotenuse

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

    5 cm · 12 cm · Pythagoras: hypotenuse

  5. 5. A right-angled triangle has perpendicular sides 60 cm and 144 cm. Find its hypotenuse.

    60 cm · 144 cm · Pythagoras: hypotenuse

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

    24 cm · 32 cm · Pythagoras: hypotenuse

  7. 7. A right-angled triangle has perpendicular sides 25 cm and 60 cm. Find its hypotenuse.

    25 cm · 60 cm · Pythagoras: hypotenuse

  8. 8. A right-angled triangle has perpendicular sides 27 cm and 36 cm. Find its hypotenuse.

    27 cm · 36 cm · Pythagoras: hypotenuse

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

    45 cm · 108 cm · Pythagoras: hypotenuse

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

    8 cm · 15 cm · Pythagoras: hypotenuse

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

    56 cm · 105 cm · Pythagoras: hypotenuse

  12. 12. A right-angled triangle has perpendicular sides 6 cm and 8 cm. Find its hypotenuse.

    6 cm · 8 cm · Pythagoras: hypotenuse
12 questions · Seed 104731 · 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 15 cm and 20 cm. Find its hypotenuse.

    25 cm

    c² = 15² + 20² = 625. Taking the positive square root gives c = 25 cm.

  2. 2. A right-angled triangle has perpendicular sides 30 cm and 40 cm. Find its hypotenuse.

    50 cm

    c² = 30² + 40² = 2500. Taking the positive square root gives c = 50 cm.

  3. 3. A right-angled triangle has perpendicular sides 55 cm and 132 cm. Find its hypotenuse.

    143 cm

    c² = 55² + 132² = 20449. Taking the positive square root gives c = 143 cm.

  4. 4. 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.

  5. 5. A right-angled triangle has perpendicular sides 60 cm and 144 cm. Find its hypotenuse.

    156 cm

    c² = 60² + 144² = 24336. Taking the positive square root gives c = 156 cm.

  6. 6. 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.

  7. 7. A right-angled triangle has perpendicular sides 25 cm and 60 cm. Find its hypotenuse.

    65 cm

    c² = 25² + 60² = 4225. Taking the positive square root gives c = 65 cm.

  8. 8. A right-angled triangle has perpendicular sides 27 cm and 36 cm. Find its hypotenuse.

    45 cm

    c² = 27² + 36² = 2025. Taking the positive square root gives c = 45 cm.

  9. 9. 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.

  10. 10. 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.

  11. 11. 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. 12. A right-angled triangle has perpendicular sides 6 cm and 8 cm. Find its hypotenuse.

    10 cm

    c² = 6² + 8² = 100. Taking the positive square root gives c = 10 cm.

12 questions · Seed 104731 · 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 15 cm and 20 cm. Find its hypotenuse.

    15 cm · 20 cm · Pythagoras: hypotenuse

  2. 2. A right-angled triangle has perpendicular sides 30 cm and 40 cm. Find its hypotenuse.

    30 cm · 40 cm · Pythagoras: hypotenuse

  3. 3. A right-angled triangle has perpendicular sides 55 cm and 132 cm. Find its hypotenuse.

    55 cm · 132 cm · Pythagoras: hypotenuse

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

    5 cm · 12 cm · Pythagoras: hypotenuse

  5. 5. A right-angled triangle has perpendicular sides 60 cm and 144 cm. Find its hypotenuse.

    60 cm · 144 cm · Pythagoras: hypotenuse

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

    24 cm · 32 cm · Pythagoras: hypotenuse

  7. 7. A right-angled triangle has perpendicular sides 25 cm and 60 cm. Find its hypotenuse.

    25 cm · 60 cm · Pythagoras: hypotenuse

  8. 8. A right-angled triangle has perpendicular sides 27 cm and 36 cm. Find its hypotenuse.

    27 cm · 36 cm · Pythagoras: hypotenuse

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

    45 cm · 108 cm · Pythagoras: hypotenuse

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

    8 cm · 15 cm · Pythagoras: hypotenuse

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

    56 cm · 105 cm · Pythagoras: hypotenuse

  12. 12. A right-angled triangle has perpendicular sides 6 cm and 8 cm. Find its hypotenuse.

    6 cm · 8 cm · Pythagoras: hypotenuse
12 questions · Seed 104731 · 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 15 cm and 20 cm. Find its hypotenuse.

    25 cm

    c² = 15² + 20² = 625. Taking the positive square root gives c = 25 cm.

  2. 2. A right-angled triangle has perpendicular sides 30 cm and 40 cm. Find its hypotenuse.

    50 cm

    c² = 30² + 40² = 2500. Taking the positive square root gives c = 50 cm.

  3. 3. A right-angled triangle has perpendicular sides 55 cm and 132 cm. Find its hypotenuse.

    143 cm

    c² = 55² + 132² = 20449. Taking the positive square root gives c = 143 cm.

  4. 4. 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.

  5. 5. A right-angled triangle has perpendicular sides 60 cm and 144 cm. Find its hypotenuse.

    156 cm

    c² = 60² + 144² = 24336. Taking the positive square root gives c = 156 cm.

  6. 6. 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.

  7. 7. A right-angled triangle has perpendicular sides 25 cm and 60 cm. Find its hypotenuse.

    65 cm

    c² = 25² + 60² = 4225. Taking the positive square root gives c = 65 cm.

  8. 8. A right-angled triangle has perpendicular sides 27 cm and 36 cm. Find its hypotenuse.

    45 cm

    c² = 27² + 36² = 2025. Taking the positive square root gives c = 45 cm.

  9. 9. 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.

  10. 10. 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.

  11. 11. 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. 12. A right-angled triangle has perpendicular sides 6 cm and 8 cm. Find its hypotenuse.

    10 cm

    c² = 6² + 8² = 100. Taking the positive square root gives c = 10 cm.

12 questions · Seed 104731 · Age guidance, not curriculum certification