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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 72 cm and 135 cm. Find its hypotenuse.

    72 cm · 135 cm · Pythagoras: hypotenuse

  2. 2. A right-angled triangle has perpendicular sides 18 cm and 24 cm. Find its hypotenuse.

    18 cm · 24 cm · Pythagoras: hypotenuse

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

    40 cm · 96 cm · Pythagoras: hypotenuse

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

    96 cm · 180 cm · Pythagoras: hypotenuse

  5. 5. A right-angled triangle has perpendicular sides 56 cm and 105 cm. Find its hypotenuse.

    56 cm · 105 cm · Pythagoras: hypotenuse

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

    50 cm · 120 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 35 cm and 84 cm. Find its hypotenuse.

    35 cm · 84 cm · Pythagoras: hypotenuse

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

    64 cm · 120 cm · Pythagoras: hypotenuse

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

    30 cm · 72 cm · Pythagoras: hypotenuse

  11. 11. A right-angled triangle has perpendicular sides 36 cm and 48 cm. Find its hypotenuse.

    36 cm · 48 cm · Pythagoras: hypotenuse

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

    12 cm · 16 cm · Pythagoras: hypotenuse
12 questions · Seed 104730 · 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 72 cm and 135 cm. Find its hypotenuse.

    153 cm

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

  2. 2. A right-angled triangle has perpendicular sides 18 cm and 24 cm. Find its hypotenuse.

    30 cm

    c² = 18² + 24² = 900. Taking the positive square root gives c = 30 cm.

  3. 3. 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.

  4. 4. 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.

  5. 5. 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.

  6. 6. 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.

  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 35 cm and 84 cm. Find its hypotenuse.

    91 cm

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

  9. 9. 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.

  10. 10. 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.

  11. 11. 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.

  12. 12. 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.

12 questions · Seed 104730 · 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 72 cm and 135 cm. Find its hypotenuse.

    72 cm · 135 cm · Pythagoras: hypotenuse

  2. 2. A right-angled triangle has perpendicular sides 18 cm and 24 cm. Find its hypotenuse.

    18 cm · 24 cm · Pythagoras: hypotenuse

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

    40 cm · 96 cm · Pythagoras: hypotenuse

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

    96 cm · 180 cm · Pythagoras: hypotenuse

  5. 5. A right-angled triangle has perpendicular sides 56 cm and 105 cm. Find its hypotenuse.

    56 cm · 105 cm · Pythagoras: hypotenuse

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

    50 cm · 120 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 35 cm and 84 cm. Find its hypotenuse.

    35 cm · 84 cm · Pythagoras: hypotenuse

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

    64 cm · 120 cm · Pythagoras: hypotenuse

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

    30 cm · 72 cm · Pythagoras: hypotenuse

  11. 11. A right-angled triangle has perpendicular sides 36 cm and 48 cm. Find its hypotenuse.

    36 cm · 48 cm · Pythagoras: hypotenuse

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

    12 cm · 16 cm · Pythagoras: hypotenuse
12 questions · Seed 104730 · 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 72 cm and 135 cm. Find its hypotenuse.

    153 cm

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

  2. 2. A right-angled triangle has perpendicular sides 18 cm and 24 cm. Find its hypotenuse.

    30 cm

    c² = 18² + 24² = 900. Taking the positive square root gives c = 30 cm.

  3. 3. 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.

  4. 4. 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.

  5. 5. 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.

  6. 6. 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.

  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 35 cm and 84 cm. Find its hypotenuse.

    91 cm

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

  9. 9. 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.

  10. 10. 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.

  11. 11. 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.

  12. 12. 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.

12 questions · Seed 104730 · Age guidance, not curriculum certification