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MathsAges 16-18

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 16-18

Pythagoras: hypotenuse

Take your time. Show your thinking.

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

    9 cm · 12 cm · Pythagoras: hypotenuse

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

    21 cm · 28 cm · Pythagoras: hypotenuse

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

    6 cm · 8 cm · Pythagoras: hypotenuse

  4. 4. A right-angled triangle has perpendicular sides 88 cm and 165 cm. Find its hypotenuse.

    88 cm · 165 cm · Pythagoras: hypotenuse

  5. 5. A right-angled triangle has perpendicular sides 30 cm and 72 cm. Find its hypotenuse.

    30 cm · 72 cm · Pythagoras: hypotenuse

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

    25 cm · 60 cm · Pythagoras: hypotenuse

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

    64 cm · 120 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 32 cm and 60 cm. Find its hypotenuse.

    32 cm · 60 cm · Pythagoras: hypotenuse

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

    15 cm · 36 cm · Pythagoras: hypotenuse

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

    40 cm · 96 cm · Pythagoras: hypotenuse

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

    16 cm · 30 cm · Pythagoras: hypotenuse
12 questions · Seed 53 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Pythagoras: hypotenuse

Answers and reasoning. Review before teaching.

  1. 1. 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.

  2. 2. 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.

  3. 3. 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.

  4. 4. A right-angled triangle has perpendicular sides 88 cm and 165 cm. Find its hypotenuse.

    187 cm

    c² = 88² + 165² = 34969. Taking the positive square root gives c = 187 cm.

  5. 5. 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.

  6. 6. 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.

  7. 7. 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.

  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 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 15 cm and 36 cm. Find its hypotenuse.

    39 cm

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

  11. 11. 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.

  12. 12. 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.

12 questions · Seed 53 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Pythagoras: hypotenuse

Take your time. Show your thinking.

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

    9 cm · 12 cm · Pythagoras: hypotenuse

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

    21 cm · 28 cm · Pythagoras: hypotenuse

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

    6 cm · 8 cm · Pythagoras: hypotenuse

  4. 4. A right-angled triangle has perpendicular sides 88 cm and 165 cm. Find its hypotenuse.

    88 cm · 165 cm · Pythagoras: hypotenuse

  5. 5. A right-angled triangle has perpendicular sides 30 cm and 72 cm. Find its hypotenuse.

    30 cm · 72 cm · Pythagoras: hypotenuse

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

    25 cm · 60 cm · Pythagoras: hypotenuse

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

    64 cm · 120 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 32 cm and 60 cm. Find its hypotenuse.

    32 cm · 60 cm · Pythagoras: hypotenuse

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

    15 cm · 36 cm · Pythagoras: hypotenuse

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

    40 cm · 96 cm · Pythagoras: hypotenuse

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

    16 cm · 30 cm · Pythagoras: hypotenuse
12 questions · Seed 53 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Pythagoras: hypotenuse

Answers and reasoning. Review before teaching.

  1. 1. 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.

  2. 2. 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.

  3. 3. 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.

  4. 4. A right-angled triangle has perpendicular sides 88 cm and 165 cm. Find its hypotenuse.

    187 cm

    c² = 88² + 165² = 34969. Taking the positive square root gives c = 187 cm.

  5. 5. 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.

  6. 6. 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.

  7. 7. 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.

  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 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 15 cm and 36 cm. Find its hypotenuse.

    39 cm

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

  11. 11. 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.

  12. 12. 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.

12 questions · Seed 53 · Age guidance, not curriculum certification