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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 21 cm and 28 cm. Find its hypotenuse.

    21 cm · 28 cm · Pythagoras: hypotenuse

  2. 2. A right-angled triangle has perpendicular sides 16 cm and 30 cm. Find its hypotenuse.

    16 cm · 30 cm · Pythagoras: hypotenuse

  3. 3. A right-angled triangle has perpendicular sides 15 cm and 20 cm. Find its hypotenuse.

    15 cm · 20 cm · Pythagoras: hypotenuse

  4. 4. A right-angled triangle has perpendicular sides 9 cm and 12 cm. Find its hypotenuse.

    9 cm · 12 cm · Pythagoras: hypotenuse

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

    35 cm · 84 cm · Pythagoras: hypotenuse

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

    24 cm · 45 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 30 cm and 72 cm. Find its hypotenuse.

    30 cm · 72 cm · Pythagoras: hypotenuse

  9. 9. A right-angled triangle has perpendicular sides 20 cm and 48 cm. Find its hypotenuse.

    20 cm · 48 cm · Pythagoras: hypotenuse

  10. 10. A right-angled triangle has perpendicular sides 40 cm and 96 cm. Find its hypotenuse.

    40 cm · 96 cm · Pythagoras: hypotenuse

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

    10 cm · 24 cm · Pythagoras: hypotenuse

  12. 12. A right-angled triangle has perpendicular sides 96 cm and 180 cm. Find its hypotenuse.

    96 cm · 180 cm · Pythagoras: hypotenuse
12 questions · Seed 44 · 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 21 cm and 28 cm. Find its hypotenuse.

    35 cm

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

  2. 2. A right-angled triangle has perpendicular sides 16 cm and 30 cm. Find its hypotenuse.

    34 cm

    c² = 16² + 30² = 1156. Taking the positive square root gives c = 34 cm.

  3. 3. 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.

  4. 4. A right-angled triangle has perpendicular sides 9 cm and 12 cm. Find its hypotenuse.

    15 cm

    c² = 9² + 12² = 225. Taking the positive square root gives c = 15 cm.

  5. 5. 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.

  6. 6. 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.

  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 30 cm and 72 cm. Find its hypotenuse.

    78 cm

    c² = 30² + 72² = 6084. Taking the positive square root gives c = 78 cm.

  9. 9. A right-angled triangle has perpendicular sides 20 cm and 48 cm. Find its hypotenuse.

    52 cm

    c² = 20² + 48² = 2704. Taking the positive square root gives c = 52 cm.

  10. 10. A right-angled triangle has perpendicular sides 40 cm and 96 cm. Find its hypotenuse.

    104 cm

    c² = 40² + 96² = 10816. Taking the positive square root gives c = 104 cm.

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

    26 cm

    c² = 10² + 24² = 676. Taking the positive square root gives c = 26 cm.

  12. 12. 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.

12 questions · Seed 44 · 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 21 cm and 28 cm. Find its hypotenuse.

    21 cm · 28 cm · Pythagoras: hypotenuse

  2. 2. A right-angled triangle has perpendicular sides 16 cm and 30 cm. Find its hypotenuse.

    16 cm · 30 cm · Pythagoras: hypotenuse

  3. 3. A right-angled triangle has perpendicular sides 15 cm and 20 cm. Find its hypotenuse.

    15 cm · 20 cm · Pythagoras: hypotenuse

  4. 4. A right-angled triangle has perpendicular sides 9 cm and 12 cm. Find its hypotenuse.

    9 cm · 12 cm · Pythagoras: hypotenuse

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

    35 cm · 84 cm · Pythagoras: hypotenuse

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

    24 cm · 45 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 30 cm and 72 cm. Find its hypotenuse.

    30 cm · 72 cm · Pythagoras: hypotenuse

  9. 9. A right-angled triangle has perpendicular sides 20 cm and 48 cm. Find its hypotenuse.

    20 cm · 48 cm · Pythagoras: hypotenuse

  10. 10. A right-angled triangle has perpendicular sides 40 cm and 96 cm. Find its hypotenuse.

    40 cm · 96 cm · Pythagoras: hypotenuse

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

    10 cm · 24 cm · Pythagoras: hypotenuse

  12. 12. A right-angled triangle has perpendicular sides 96 cm and 180 cm. Find its hypotenuse.

    96 cm · 180 cm · Pythagoras: hypotenuse
12 questions · Seed 44 · 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 21 cm and 28 cm. Find its hypotenuse.

    35 cm

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

  2. 2. A right-angled triangle has perpendicular sides 16 cm and 30 cm. Find its hypotenuse.

    34 cm

    c² = 16² + 30² = 1156. Taking the positive square root gives c = 34 cm.

  3. 3. 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.

  4. 4. A right-angled triangle has perpendicular sides 9 cm and 12 cm. Find its hypotenuse.

    15 cm

    c² = 9² + 12² = 225. Taking the positive square root gives c = 15 cm.

  5. 5. 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.

  6. 6. 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.

  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 30 cm and 72 cm. Find its hypotenuse.

    78 cm

    c² = 30² + 72² = 6084. Taking the positive square root gives c = 78 cm.

  9. 9. A right-angled triangle has perpendicular sides 20 cm and 48 cm. Find its hypotenuse.

    52 cm

    c² = 20² + 48² = 2704. Taking the positive square root gives c = 52 cm.

  10. 10. A right-angled triangle has perpendicular sides 40 cm and 96 cm. Find its hypotenuse.

    104 cm

    c² = 40² + 96² = 10816. Taking the positive square root gives c = 104 cm.

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

    26 cm

    c² = 10² + 24² = 676. Taking the positive square root gives c = 26 cm.

  12. 12. 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.

12 questions · Seed 44 · Age guidance, not curriculum certification