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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 96 cm and 180 cm. Find its hypotenuse.

    96 cm · 180 cm · Pythagoras: hypotenuse

  2. 2. A right-angled triangle has perpendicular sides 12 cm and 16 cm. Find its hypotenuse.

    12 cm · 16 cm · Pythagoras: hypotenuse

  3. 3. A right-angled triangle has perpendicular sides 48 cm and 90 cm. Find its hypotenuse.

    48 cm · 90 cm · Pythagoras: hypotenuse

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

    6 cm · 8 cm · Pythagoras: hypotenuse

  5. 5. A right-angled triangle has perpendicular sides 72 cm and 135 cm. Find its hypotenuse.

    72 cm · 135 cm · Pythagoras: hypotenuse

  6. 6. A right-angled triangle has perpendicular sides 35 cm and 84 cm. Find its hypotenuse.

    35 cm · 84 cm · Pythagoras: hypotenuse

  7. 7. A right-angled triangle has perpendicular sides 3 cm and 4 cm. Find its hypotenuse.

    3 cm · 4 cm · Pythagoras: hypotenuse

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

    33 cm · 44 cm · Pythagoras: hypotenuse

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

    32 cm · 60 cm · Pythagoras: hypotenuse

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

    30 cm · 40 cm · Pythagoras: hypotenuse

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

    55 cm · 132 cm · Pythagoras: hypotenuse

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

    8 cm · 15 cm · Pythagoras: hypotenuse
12 questions · Seed 46 · 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 96 cm and 180 cm. Find its hypotenuse.

    204 cm

    c² = 96² + 180² = 41616. Taking the positive square root gives c = 204 cm.

  2. 2. A right-angled triangle has perpendicular sides 12 cm and 16 cm. Find its hypotenuse.

    20 cm

    c² = 12² + 16² = 400. Taking the positive square root gives c = 20 cm.

  3. 3. A right-angled triangle has perpendicular sides 48 cm and 90 cm. Find its hypotenuse.

    102 cm

    c² = 48² + 90² = 10404. Taking the positive square root gives c = 102 cm.

  4. 4. 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.

  5. 5. A right-angled triangle has perpendicular sides 72 cm and 135 cm. Find its hypotenuse.

    153 cm

    c² = 72² + 135² = 23409. Taking the positive square root gives c = 153 cm.

  6. 6. A right-angled triangle has perpendicular sides 35 cm and 84 cm. Find its hypotenuse.

    91 cm

    c² = 35² + 84² = 8281. Taking the positive square root gives c = 91 cm.

  7. 7. A right-angled triangle has perpendicular sides 3 cm and 4 cm. Find its hypotenuse.

    5 cm

    c² = 3² + 4² = 25. Taking the positive square root gives c = 5 cm.

  8. 8. 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.

  9. 9. 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.

  10. 10. 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.

  11. 11. 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.

  12. 12. 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.

12 questions · Seed 46 · 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 96 cm and 180 cm. Find its hypotenuse.

    96 cm · 180 cm · Pythagoras: hypotenuse

  2. 2. A right-angled triangle has perpendicular sides 12 cm and 16 cm. Find its hypotenuse.

    12 cm · 16 cm · Pythagoras: hypotenuse

  3. 3. A right-angled triangle has perpendicular sides 48 cm and 90 cm. Find its hypotenuse.

    48 cm · 90 cm · Pythagoras: hypotenuse

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

    6 cm · 8 cm · Pythagoras: hypotenuse

  5. 5. A right-angled triangle has perpendicular sides 72 cm and 135 cm. Find its hypotenuse.

    72 cm · 135 cm · Pythagoras: hypotenuse

  6. 6. A right-angled triangle has perpendicular sides 35 cm and 84 cm. Find its hypotenuse.

    35 cm · 84 cm · Pythagoras: hypotenuse

  7. 7. A right-angled triangle has perpendicular sides 3 cm and 4 cm. Find its hypotenuse.

    3 cm · 4 cm · Pythagoras: hypotenuse

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

    33 cm · 44 cm · Pythagoras: hypotenuse

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

    32 cm · 60 cm · Pythagoras: hypotenuse

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

    30 cm · 40 cm · Pythagoras: hypotenuse

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

    55 cm · 132 cm · Pythagoras: hypotenuse

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

    8 cm · 15 cm · Pythagoras: hypotenuse
12 questions · Seed 46 · 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 96 cm and 180 cm. Find its hypotenuse.

    204 cm

    c² = 96² + 180² = 41616. Taking the positive square root gives c = 204 cm.

  2. 2. A right-angled triangle has perpendicular sides 12 cm and 16 cm. Find its hypotenuse.

    20 cm

    c² = 12² + 16² = 400. Taking the positive square root gives c = 20 cm.

  3. 3. A right-angled triangle has perpendicular sides 48 cm and 90 cm. Find its hypotenuse.

    102 cm

    c² = 48² + 90² = 10404. Taking the positive square root gives c = 102 cm.

  4. 4. 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.

  5. 5. A right-angled triangle has perpendicular sides 72 cm and 135 cm. Find its hypotenuse.

    153 cm

    c² = 72² + 135² = 23409. Taking the positive square root gives c = 153 cm.

  6. 6. A right-angled triangle has perpendicular sides 35 cm and 84 cm. Find its hypotenuse.

    91 cm

    c² = 35² + 84² = 8281. Taking the positive square root gives c = 91 cm.

  7. 7. A right-angled triangle has perpendicular sides 3 cm and 4 cm. Find its hypotenuse.

    5 cm

    c² = 3² + 4² = 25. Taking the positive square root gives c = 5 cm.

  8. 8. 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.

  9. 9. 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.

  10. 10. 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.

  11. 11. 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.

  12. 12. 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.

12 questions · Seed 46 · Age guidance, not curriculum certification