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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 18 cm and 24 cm. Find its hypotenuse.

    18 cm · 24 cm · Pythagoras: hypotenuse

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

    36 cm · 48 cm · Pythagoras: hypotenuse

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

    5 cm · 12 cm · Pythagoras: hypotenuse

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

    3 cm · 4 cm · Pythagoras: hypotenuse

  5. 5. A right-angled triangle has perpendicular sides 27 cm and 36 cm. Find its hypotenuse.

    27 cm · 36 cm · Pythagoras: hypotenuse

  6. 6. A right-angled triangle has perpendicular sides 16 cm and 30 cm. Find its hypotenuse.

    16 cm · 30 cm · Pythagoras: hypotenuse

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

    15 cm · 20 cm · Pythagoras: hypotenuse

  8. 8. A right-angled triangle has perpendicular sides 24 cm and 45 cm. Find its hypotenuse.

    24 cm · 45 cm · Pythagoras: hypotenuse

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

    9 cm · 12 cm · Pythagoras: hypotenuse

  10. 10. A right-angled triangle has perpendicular sides 55 cm and 132 cm. Find its hypotenuse.

    55 cm · 132 cm · Pythagoras: hypotenuse

  11. 11. A right-angled triangle has perpendicular sides 6 cm and 8 cm. Find its hypotenuse.

    6 cm · 8 cm · Pythagoras: hypotenuse

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

    88 cm · 165 cm · Pythagoras: hypotenuse
12 questions · Seed 58 · 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 18 cm and 24 cm. Find its hypotenuse.

    30 cm

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

  2. 2. 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.

  3. 3. 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.

  4. 4. 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.

  5. 5. 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.

  6. 6. 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.

  7. 7. 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.

  8. 8. A right-angled triangle has perpendicular sides 24 cm and 45 cm. Find its hypotenuse.

    51 cm

    c² = 24² + 45² = 2601. Taking the positive square root gives c = 51 cm.

  9. 9. 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.

  10. 10. 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.

  11. 11. A right-angled triangle has perpendicular sides 6 cm and 8 cm. Find its hypotenuse.

    10 cm

    c² = 6² + 8² = 100. Taking the positive square root gives c = 10 cm.

  12. 12. 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.

12 questions · Seed 58 · 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 18 cm and 24 cm. Find its hypotenuse.

    18 cm · 24 cm · Pythagoras: hypotenuse

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

    36 cm · 48 cm · Pythagoras: hypotenuse

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

    5 cm · 12 cm · Pythagoras: hypotenuse

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

    3 cm · 4 cm · Pythagoras: hypotenuse

  5. 5. A right-angled triangle has perpendicular sides 27 cm and 36 cm. Find its hypotenuse.

    27 cm · 36 cm · Pythagoras: hypotenuse

  6. 6. A right-angled triangle has perpendicular sides 16 cm and 30 cm. Find its hypotenuse.

    16 cm · 30 cm · Pythagoras: hypotenuse

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

    15 cm · 20 cm · Pythagoras: hypotenuse

  8. 8. A right-angled triangle has perpendicular sides 24 cm and 45 cm. Find its hypotenuse.

    24 cm · 45 cm · Pythagoras: hypotenuse

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

    9 cm · 12 cm · Pythagoras: hypotenuse

  10. 10. A right-angled triangle has perpendicular sides 55 cm and 132 cm. Find its hypotenuse.

    55 cm · 132 cm · Pythagoras: hypotenuse

  11. 11. A right-angled triangle has perpendicular sides 6 cm and 8 cm. Find its hypotenuse.

    6 cm · 8 cm · Pythagoras: hypotenuse

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

    88 cm · 165 cm · Pythagoras: hypotenuse
12 questions · Seed 58 · 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 18 cm and 24 cm. Find its hypotenuse.

    30 cm

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

  2. 2. 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.

  3. 3. 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.

  4. 4. 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.

  5. 5. 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.

  6. 6. 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.

  7. 7. 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.

  8. 8. A right-angled triangle has perpendicular sides 24 cm and 45 cm. Find its hypotenuse.

    51 cm

    c² = 24² + 45² = 2601. Taking the positive square root gives c = 51 cm.

  9. 9. 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.

  10. 10. 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.

  11. 11. A right-angled triangle has perpendicular sides 6 cm and 8 cm. Find its hypotenuse.

    10 cm

    c² = 6² + 8² = 100. Taking the positive square root gives c = 10 cm.

  12. 12. 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.

12 questions · Seed 58 · Age guidance, not curriculum certification