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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 45 cm and 108 cm. Find its hypotenuse.

    45 cm · 108 cm · Pythagoras: hypotenuse

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

    80 cm · 150 cm · Pythagoras: hypotenuse

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

    6 cm · 8 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 36 cm and 48 cm. Find its hypotenuse.

    36 cm · 48 cm · Pythagoras: hypotenuse

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

    88 cm · 165 cm · Pythagoras: hypotenuse

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

    12 cm · 16 cm · Pythagoras: hypotenuse

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

    64 cm · 120 cm · Pythagoras: hypotenuse

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

    60 cm · 144 cm · Pythagoras: hypotenuse

  10. 10. A right-angled triangle has perpendicular sides 21 cm and 28 cm. Find its hypotenuse.

    21 cm · 28 cm · Pythagoras: hypotenuse

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

    27 cm · 36 cm · Pythagoras: hypotenuse

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

    56 cm · 105 cm · Pythagoras: hypotenuse
12 questions · Seed 47 · 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 45 cm and 108 cm. Find its hypotenuse.

    117 cm

    c² = 45² + 108² = 13689. Taking the positive square root gives c = 117 cm.

  2. 2. 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.

  3. 3. 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.

  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 36 cm and 48 cm. Find its hypotenuse.

    60 cm

    c² = 36² + 48² = 3600. Taking the positive square root gives c = 60 cm.

  6. 6. 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.

  7. 7. 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.

  8. 8. 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.

  9. 9. 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.

  10. 10. A right-angled triangle has perpendicular sides 21 cm and 28 cm. Find its hypotenuse.

    35 cm

    c² = 21² + 28² = 1225. Taking the positive square root gives c = 35 cm.

  11. 11. 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.

  12. 12. 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 questions · Seed 47 · 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 45 cm and 108 cm. Find its hypotenuse.

    45 cm · 108 cm · Pythagoras: hypotenuse

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

    80 cm · 150 cm · Pythagoras: hypotenuse

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

    6 cm · 8 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 36 cm and 48 cm. Find its hypotenuse.

    36 cm · 48 cm · Pythagoras: hypotenuse

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

    88 cm · 165 cm · Pythagoras: hypotenuse

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

    12 cm · 16 cm · Pythagoras: hypotenuse

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

    64 cm · 120 cm · Pythagoras: hypotenuse

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

    60 cm · 144 cm · Pythagoras: hypotenuse

  10. 10. A right-angled triangle has perpendicular sides 21 cm and 28 cm. Find its hypotenuse.

    21 cm · 28 cm · Pythagoras: hypotenuse

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

    27 cm · 36 cm · Pythagoras: hypotenuse

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

    56 cm · 105 cm · Pythagoras: hypotenuse
12 questions · Seed 47 · 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 45 cm and 108 cm. Find its hypotenuse.

    117 cm

    c² = 45² + 108² = 13689. Taking the positive square root gives c = 117 cm.

  2. 2. 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.

  3. 3. 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.

  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 36 cm and 48 cm. Find its hypotenuse.

    60 cm

    c² = 36² + 48² = 3600. Taking the positive square root gives c = 60 cm.

  6. 6. 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.

  7. 7. 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.

  8. 8. 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.

  9. 9. 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.

  10. 10. A right-angled triangle has perpendicular sides 21 cm and 28 cm. Find its hypotenuse.

    35 cm

    c² = 21² + 28² = 1225. Taking the positive square root gives c = 35 cm.

  11. 11. 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.

  12. 12. 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 questions · Seed 47 · Age guidance, not curriculum certification