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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 80 cm and 150 cm. Find its hypotenuse.

    80 cm · 150 cm · Pythagoras: hypotenuse

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

    55 cm · 132 cm · Pythagoras: hypotenuse

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

    30 cm · 40 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 40 cm and 75 cm. Find its hypotenuse.

    40 cm · 75 cm · Pythagoras: hypotenuse

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

    18 cm · 24 cm · Pythagoras: hypotenuse

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

    64 cm · 120 cm · Pythagoras: hypotenuse

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

    6 cm · 8 cm · Pythagoras: hypotenuse

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

    56 cm · 105 cm · Pythagoras: hypotenuse

  10. 10. A right-angled triangle has perpendicular sides 33 cm and 44 cm. Find its hypotenuse.

    33 cm · 44 cm · Pythagoras: hypotenuse

  11. 11. A right-angled triangle has perpendicular sides 24 cm and 32 cm. Find its hypotenuse.

    24 cm · 32 cm · Pythagoras: hypotenuse

  12. 12. A right-angled triangle has perpendicular sides 20 cm and 48 cm. Find its hypotenuse.

    20 cm · 48 cm · Pythagoras: hypotenuse
12 questions · Seed 57 · 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 80 cm and 150 cm. Find its hypotenuse.

    170 cm

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

  2. 2. 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.

  3. 3. 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.

  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 40 cm and 75 cm. Find its hypotenuse.

    85 cm

    c² = 40² + 75² = 7225. Taking the positive square root gives c = 85 cm.

  6. 6. 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.

  7. 7. 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.

  8. 8. 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.

  9. 9. 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.

  10. 10. A right-angled triangle has perpendicular sides 33 cm and 44 cm. Find its hypotenuse.

    55 cm

    c² = 33² + 44² = 3025. Taking the positive square root gives c = 55 cm.

  11. 11. A right-angled triangle has perpendicular sides 24 cm and 32 cm. Find its hypotenuse.

    40 cm

    c² = 24² + 32² = 1600. Taking the positive square root gives c = 40 cm.

  12. 12. A right-angled triangle has perpendicular sides 20 cm and 48 cm. Find its hypotenuse.

    52 cm

    c² = 20² + 48² = 2704. Taking the positive square root gives c = 52 cm.

12 questions · Seed 57 · 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 80 cm and 150 cm. Find its hypotenuse.

    80 cm · 150 cm · Pythagoras: hypotenuse

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

    55 cm · 132 cm · Pythagoras: hypotenuse

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

    30 cm · 40 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 40 cm and 75 cm. Find its hypotenuse.

    40 cm · 75 cm · Pythagoras: hypotenuse

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

    18 cm · 24 cm · Pythagoras: hypotenuse

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

    64 cm · 120 cm · Pythagoras: hypotenuse

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

    6 cm · 8 cm · Pythagoras: hypotenuse

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

    56 cm · 105 cm · Pythagoras: hypotenuse

  10. 10. A right-angled triangle has perpendicular sides 33 cm and 44 cm. Find its hypotenuse.

    33 cm · 44 cm · Pythagoras: hypotenuse

  11. 11. A right-angled triangle has perpendicular sides 24 cm and 32 cm. Find its hypotenuse.

    24 cm · 32 cm · Pythagoras: hypotenuse

  12. 12. A right-angled triangle has perpendicular sides 20 cm and 48 cm. Find its hypotenuse.

    20 cm · 48 cm · Pythagoras: hypotenuse
12 questions · Seed 57 · 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 80 cm and 150 cm. Find its hypotenuse.

    170 cm

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

  2. 2. 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.

  3. 3. 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.

  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 40 cm and 75 cm. Find its hypotenuse.

    85 cm

    c² = 40² + 75² = 7225. Taking the positive square root gives c = 85 cm.

  6. 6. 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.

  7. 7. 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.

  8. 8. 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.

  9. 9. 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.

  10. 10. A right-angled triangle has perpendicular sides 33 cm and 44 cm. Find its hypotenuse.

    55 cm

    c² = 33² + 44² = 3025. Taking the positive square root gives c = 55 cm.

  11. 11. A right-angled triangle has perpendicular sides 24 cm and 32 cm. Find its hypotenuse.

    40 cm

    c² = 24² + 32² = 1600. Taking the positive square root gives c = 40 cm.

  12. 12. A right-angled triangle has perpendicular sides 20 cm and 48 cm. Find its hypotenuse.

    52 cm

    c² = 20² + 48² = 2704. Taking the positive square root gives c = 52 cm.

12 questions · Seed 57 · Age guidance, not curriculum certification