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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 5 cm and 12 cm. Find its hypotenuse.

    5 cm · 12 cm · Pythagoras: hypotenuse

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

    10 cm · 24 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 64 cm and 120 cm. Find its hypotenuse.

    64 cm · 120 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 40 cm and 75 cm. Find its hypotenuse.

    40 cm · 75 cm · Pythagoras: hypotenuse

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

    32 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 36 cm and 48 cm. Find its hypotenuse.

    36 cm · 48 cm · Pythagoras: hypotenuse

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

    21 cm · 28 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 24 cm and 32 cm. Find its hypotenuse.

    24 cm · 32 cm · Pythagoras: hypotenuse
12 questions · Seed 56 · 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 5 cm and 12 cm. Find its hypotenuse.

    13 cm

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

  2. 2. 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.

  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 64 cm and 120 cm. Find its hypotenuse.

    136 cm

    c² = 64² + 120² = 18496. Taking the positive square root gives c = 136 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 40 cm and 75 cm. Find its hypotenuse.

    85 cm

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

  7. 7. 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.

  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 36 cm and 48 cm. Find its hypotenuse.

    60 cm

    c² = 36² + 48² = 3600. Taking the positive square root gives c = 60 cm.

  10. 10. 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.

  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 24 cm and 32 cm. Find its hypotenuse.

    40 cm

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

12 questions · Seed 56 · 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 5 cm and 12 cm. Find its hypotenuse.

    5 cm · 12 cm · Pythagoras: hypotenuse

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

    10 cm · 24 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 64 cm and 120 cm. Find its hypotenuse.

    64 cm · 120 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 40 cm and 75 cm. Find its hypotenuse.

    40 cm · 75 cm · Pythagoras: hypotenuse

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

    32 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 36 cm and 48 cm. Find its hypotenuse.

    36 cm · 48 cm · Pythagoras: hypotenuse

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

    21 cm · 28 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 24 cm and 32 cm. Find its hypotenuse.

    24 cm · 32 cm · Pythagoras: hypotenuse
12 questions · Seed 56 · 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 5 cm and 12 cm. Find its hypotenuse.

    13 cm

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

  2. 2. 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.

  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 64 cm and 120 cm. Find its hypotenuse.

    136 cm

    c² = 64² + 120² = 18496. Taking the positive square root gives c = 136 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 40 cm and 75 cm. Find its hypotenuse.

    85 cm

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

  7. 7. 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.

  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 36 cm and 48 cm. Find its hypotenuse.

    60 cm

    c² = 36² + 48² = 3600. Taking the positive square root gives c = 60 cm.

  10. 10. 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.

  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 24 cm and 32 cm. Find its hypotenuse.

    40 cm

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

12 questions · Seed 56 · Age guidance, not curriculum certification