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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 15 cm and 36 cm. Find its hypotenuse.

    15 cm · 36 cm · Pythagoras: hypotenuse

  2. 2. A right-angled triangle has perpendicular sides 60 cm and 144 cm. Find its hypotenuse.

    60 cm · 144 cm · Pythagoras: hypotenuse

  3. 3. A right-angled triangle has perpendicular sides 3 cm and 4 cm. Find its hypotenuse.

    3 cm · 4 cm · Pythagoras: hypotenuse

  4. 4. A right-angled triangle has perpendicular sides 80 cm and 150 cm. Find its hypotenuse.

    80 cm · 150 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 15 cm and 20 cm. Find its hypotenuse.

    15 cm · 20 cm · Pythagoras: hypotenuse

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

    36 cm · 48 cm · Pythagoras: hypotenuse

  8. 8. A right-angled triangle has perpendicular sides 72 cm and 135 cm. Find its hypotenuse.

    72 cm · 135 cm · Pythagoras: hypotenuse

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

    10 cm · 24 cm · Pythagoras: hypotenuse

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

    32 cm · 60 cm · Pythagoras: hypotenuse

  11. 11. A right-angled triangle has perpendicular sides 40 cm and 75 cm. Find its hypotenuse.

    40 cm · 75 cm · Pythagoras: hypotenuse

  12. 12. A right-angled triangle has perpendicular sides 30 cm and 40 cm. Find its hypotenuse.

    30 cm · 40 cm · Pythagoras: hypotenuse
12 questions · Seed 50 · 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 15 cm and 36 cm. Find its hypotenuse.

    39 cm

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

  2. 2. A right-angled triangle has perpendicular sides 60 cm and 144 cm. Find its hypotenuse.

    156 cm

    c² = 60² + 144² = 24336. Taking the positive square root gives c = 156 cm.

  3. 3. 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.

  4. 4. A right-angled triangle has perpendicular sides 80 cm and 150 cm. Find its hypotenuse.

    170 cm

    c² = 80² + 150² = 28900. Taking the positive square root gives c = 170 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 15 cm and 20 cm. Find its hypotenuse.

    25 cm

    c² = 15² + 20² = 625. Taking the positive square root gives c = 25 cm.

  7. 7. 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.

  8. 8. 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.

  9. 9. 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.

  10. 10. 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.

  11. 11. 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.

  12. 12. A right-angled triangle has perpendicular sides 30 cm and 40 cm. Find its hypotenuse.

    50 cm

    c² = 30² + 40² = 2500. Taking the positive square root gives c = 50 cm.

12 questions · Seed 50 · 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 15 cm and 36 cm. Find its hypotenuse.

    15 cm · 36 cm · Pythagoras: hypotenuse

  2. 2. A right-angled triangle has perpendicular sides 60 cm and 144 cm. Find its hypotenuse.

    60 cm · 144 cm · Pythagoras: hypotenuse

  3. 3. A right-angled triangle has perpendicular sides 3 cm and 4 cm. Find its hypotenuse.

    3 cm · 4 cm · Pythagoras: hypotenuse

  4. 4. A right-angled triangle has perpendicular sides 80 cm and 150 cm. Find its hypotenuse.

    80 cm · 150 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 15 cm and 20 cm. Find its hypotenuse.

    15 cm · 20 cm · Pythagoras: hypotenuse

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

    36 cm · 48 cm · Pythagoras: hypotenuse

  8. 8. A right-angled triangle has perpendicular sides 72 cm and 135 cm. Find its hypotenuse.

    72 cm · 135 cm · Pythagoras: hypotenuse

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

    10 cm · 24 cm · Pythagoras: hypotenuse

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

    32 cm · 60 cm · Pythagoras: hypotenuse

  11. 11. A right-angled triangle has perpendicular sides 40 cm and 75 cm. Find its hypotenuse.

    40 cm · 75 cm · Pythagoras: hypotenuse

  12. 12. A right-angled triangle has perpendicular sides 30 cm and 40 cm. Find its hypotenuse.

    30 cm · 40 cm · Pythagoras: hypotenuse
12 questions · Seed 50 · 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 15 cm and 36 cm. Find its hypotenuse.

    39 cm

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

  2. 2. A right-angled triangle has perpendicular sides 60 cm and 144 cm. Find its hypotenuse.

    156 cm

    c² = 60² + 144² = 24336. Taking the positive square root gives c = 156 cm.

  3. 3. 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.

  4. 4. A right-angled triangle has perpendicular sides 80 cm and 150 cm. Find its hypotenuse.

    170 cm

    c² = 80² + 150² = 28900. Taking the positive square root gives c = 170 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 15 cm and 20 cm. Find its hypotenuse.

    25 cm

    c² = 15² + 20² = 625. Taking the positive square root gives c = 25 cm.

  7. 7. 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.

  8. 8. 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.

  9. 9. 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.

  10. 10. 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.

  11. 11. 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.

  12. 12. A right-angled triangle has perpendicular sides 30 cm and 40 cm. Find its hypotenuse.

    50 cm

    c² = 30² + 40² = 2500. Taking the positive square root gives c = 50 cm.

12 questions · Seed 50 · Age guidance, not curriculum certification