Small practice. Bright discoveries.Explore the free starter collection
worksheetstudio.
Sign in
Back to worksheets
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.

New variationTry interactive challengeBrowse templates
Age band:Ages 13-15Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 13-15

Pythagoras: hypotenuse

Take your time. Show your thinking.

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

    9 cm · 12 cm · Pythagoras: hypotenuse

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

    32 cm · 60 cm · Pythagoras: hypotenuse

  3. 3. A right-angled triangle has perpendicular sides 8 cm and 15 cm. Find its hypotenuse.

    8 cm · 15 cm · Pythagoras: hypotenuse

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

    6 cm · 8 cm · Pythagoras: hypotenuse

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

    15 cm · 20 cm · Pythagoras: hypotenuse

  6. 6. A right-angled triangle has perpendicular sides 25 cm and 60 cm. Find its hypotenuse.

    25 cm · 60 cm · Pythagoras: hypotenuse

  7. 7. A right-angled triangle has perpendicular sides 45 cm and 108 cm. Find its hypotenuse.

    45 cm · 108 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 21 cm and 28 cm. Find its hypotenuse.

    21 cm · 28 cm · Pythagoras: hypotenuse

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

    15 cm · 36 cm · Pythagoras: hypotenuse

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

    72 cm · 135 cm · Pythagoras: hypotenuse

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

    18 cm · 24 cm · Pythagoras: hypotenuse
12 questions · Seed 51 · 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 9 cm and 12 cm. Find its hypotenuse.

    15 cm

    c² = 9² + 12² = 225. Taking the positive square root gives c = 15 cm.

  2. 2. 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.

  3. 3. A right-angled triangle has perpendicular sides 8 cm and 15 cm. Find its hypotenuse.

    17 cm

    c² = 8² + 15² = 289. Taking the positive square root gives c = 17 cm.

  4. 4. 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.

  5. 5. 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.

  6. 6. A right-angled triangle has perpendicular sides 25 cm and 60 cm. Find its hypotenuse.

    65 cm

    c² = 25² + 60² = 4225. Taking the positive square root gives c = 65 cm.

  7. 7. 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.

  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 21 cm and 28 cm. Find its hypotenuse.

    35 cm

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

  10. 10. 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.

  11. 11. 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.

  12. 12. 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.

12 questions · Seed 51 · 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 9 cm and 12 cm. Find its hypotenuse.

    9 cm · 12 cm · Pythagoras: hypotenuse

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

    32 cm · 60 cm · Pythagoras: hypotenuse

  3. 3. A right-angled triangle has perpendicular sides 8 cm and 15 cm. Find its hypotenuse.

    8 cm · 15 cm · Pythagoras: hypotenuse

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

    6 cm · 8 cm · Pythagoras: hypotenuse

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

    15 cm · 20 cm · Pythagoras: hypotenuse

  6. 6. A right-angled triangle has perpendicular sides 25 cm and 60 cm. Find its hypotenuse.

    25 cm · 60 cm · Pythagoras: hypotenuse

  7. 7. A right-angled triangle has perpendicular sides 45 cm and 108 cm. Find its hypotenuse.

    45 cm · 108 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 21 cm and 28 cm. Find its hypotenuse.

    21 cm · 28 cm · Pythagoras: hypotenuse

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

    15 cm · 36 cm · Pythagoras: hypotenuse

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

    72 cm · 135 cm · Pythagoras: hypotenuse

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

    18 cm · 24 cm · Pythagoras: hypotenuse
12 questions · Seed 51 · 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 9 cm and 12 cm. Find its hypotenuse.

    15 cm

    c² = 9² + 12² = 225. Taking the positive square root gives c = 15 cm.

  2. 2. 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.

  3. 3. A right-angled triangle has perpendicular sides 8 cm and 15 cm. Find its hypotenuse.

    17 cm

    c² = 8² + 15² = 289. Taking the positive square root gives c = 17 cm.

  4. 4. 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.

  5. 5. 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.

  6. 6. A right-angled triangle has perpendicular sides 25 cm and 60 cm. Find its hypotenuse.

    65 cm

    c² = 25² + 60² = 4225. Taking the positive square root gives c = 65 cm.

  7. 7. 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.

  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 21 cm and 28 cm. Find its hypotenuse.

    35 cm

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

  10. 10. 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.

  11. 11. 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.

  12. 12. 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.

12 questions · Seed 51 · Age guidance, not curriculum certification