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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 16 cm and 30 cm. Find its hypotenuse.

    16 cm · 30 cm · Pythagoras: hypotenuse

  2. 2. A right-angled triangle has perpendicular sides 15 cm and 20 cm. Find its hypotenuse.

    15 cm · 20 cm · Pythagoras: hypotenuse

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

    15 cm · 36 cm · Pythagoras: hypotenuse

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

    72 cm · 135 cm · Pythagoras: hypotenuse

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

    9 cm · 12 cm · Pythagoras: hypotenuse

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

    3 cm · 4 cm · Pythagoras: hypotenuse

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

    88 cm · 165 cm · Pythagoras: hypotenuse

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

    96 cm · 180 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 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 80 cm and 150 cm. Find its hypotenuse.

    80 cm · 150 cm · Pythagoras: hypotenuse
12 questions · Seed 59 · 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 16 cm and 30 cm. Find its hypotenuse.

    34 cm

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

  2. 2. 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.

  3. 3. 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.

  4. 4. 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.

  5. 5. 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.

  6. 6. 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.

  7. 7. 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.

  8. 8. 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.

  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 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 80 cm and 150 cm. Find its hypotenuse.

    170 cm

    c² = 80² + 150² = 28900. Taking the positive square root gives c = 170 cm.

12 questions · Seed 59 · 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 16 cm and 30 cm. Find its hypotenuse.

    16 cm · 30 cm · Pythagoras: hypotenuse

  2. 2. A right-angled triangle has perpendicular sides 15 cm and 20 cm. Find its hypotenuse.

    15 cm · 20 cm · Pythagoras: hypotenuse

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

    15 cm · 36 cm · Pythagoras: hypotenuse

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

    72 cm · 135 cm · Pythagoras: hypotenuse

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

    9 cm · 12 cm · Pythagoras: hypotenuse

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

    3 cm · 4 cm · Pythagoras: hypotenuse

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

    88 cm · 165 cm · Pythagoras: hypotenuse

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

    96 cm · 180 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 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 80 cm and 150 cm. Find its hypotenuse.

    80 cm · 150 cm · Pythagoras: hypotenuse
12 questions · Seed 59 · 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 16 cm and 30 cm. Find its hypotenuse.

    34 cm

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

  2. 2. 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.

  3. 3. 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.

  4. 4. 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.

  5. 5. 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.

  6. 6. 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.

  7. 7. 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.

  8. 8. 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.

  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 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 80 cm and 150 cm. Find its hypotenuse.

    170 cm

    c² = 80² + 150² = 28900. Taking the positive square root gives c = 170 cm.

12 questions · Seed 59 · Age guidance, not curriculum certification