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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 3 cm and 4 cm. Find its hypotenuse.

    3 cm · 4 cm · Pythagoras: hypotenuse

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

    9 cm · 12 cm · Pythagoras: hypotenuse

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

    20 cm · 48 cm · Pythagoras: hypotenuse

  4. 4. A right-angled triangle has perpendicular sides 50 cm and 120 cm. Find its hypotenuse.

    50 cm · 120 cm · Pythagoras: hypotenuse

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

    10 cm · 24 cm · Pythagoras: hypotenuse

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

    12 cm · 16 cm · Pythagoras: hypotenuse

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

    30 cm · 72 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 16 cm and 30 cm. Find its hypotenuse.

    16 cm · 30 cm · Pythagoras: hypotenuse

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

    33 cm · 44 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 96 cm and 180 cm. Find its hypotenuse.

    96 cm · 180 cm · Pythagoras: hypotenuse
12 questions · Seed 49 · 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 3 cm and 4 cm. Find its hypotenuse.

    5 cm

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

  2. 2. 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.

  3. 3. 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.

  4. 4. A right-angled triangle has perpendicular sides 50 cm and 120 cm. Find its hypotenuse.

    130 cm

    c² = 50² + 120² = 16900. Taking the positive square root gives c = 130 cm.

  5. 5. 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.

  6. 6. 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.

  7. 7. 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.

  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 16 cm and 30 cm. Find its hypotenuse.

    34 cm

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

  10. 10. 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.

  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 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 49 · 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 3 cm and 4 cm. Find its hypotenuse.

    3 cm · 4 cm · Pythagoras: hypotenuse

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

    9 cm · 12 cm · Pythagoras: hypotenuse

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

    20 cm · 48 cm · Pythagoras: hypotenuse

  4. 4. A right-angled triangle has perpendicular sides 50 cm and 120 cm. Find its hypotenuse.

    50 cm · 120 cm · Pythagoras: hypotenuse

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

    10 cm · 24 cm · Pythagoras: hypotenuse

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

    12 cm · 16 cm · Pythagoras: hypotenuse

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

    30 cm · 72 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 16 cm and 30 cm. Find its hypotenuse.

    16 cm · 30 cm · Pythagoras: hypotenuse

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

    33 cm · 44 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 96 cm and 180 cm. Find its hypotenuse.

    96 cm · 180 cm · Pythagoras: hypotenuse
12 questions · Seed 49 · 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 3 cm and 4 cm. Find its hypotenuse.

    5 cm

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

  2. 2. 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.

  3. 3. 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.

  4. 4. A right-angled triangle has perpendicular sides 50 cm and 120 cm. Find its hypotenuse.

    130 cm

    c² = 50² + 120² = 16900. Taking the positive square root gives c = 130 cm.

  5. 5. 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.

  6. 6. 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.

  7. 7. 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.

  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 16 cm and 30 cm. Find its hypotenuse.

    34 cm

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

  10. 10. 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.

  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 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 49 · Age guidance, not curriculum certification