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Class 9–10 Maths: Pythagoras theorem practice questions

Practise pythagoras theorem for Classes 9 and 10. Try the 10-question quiz below and see each answer explained straight away, then read all 12 worked examples with answers underneath. Free, no sign-up.

Pythagoras theorem: worked examples with answers

These Maths questions are generated, so a fresh set appears every time you press "Practise more questions". Here are some worked examples.

1. A right-angled triangle has legs of 60 cm and 63 cm. How long is the hypotenuse?

   1. A. 174 cm
   2. B. 87 cm ✓
   3. C. 123 cm
   4. D. 88 cm

   Answer: 87 cm. c² = 60² + 63² = 3600 + 3969 = 7569, so c = 87 cm.

2. A right-angled triangle has legs of 6 cm and 8 cm. How long is the hypotenuse?

   1. A. 10 cm ✓
   2. B. 9 cm
   3. C. 11 cm
   4. D. 2 cm

   Answer: 10 cm. c² = 6² + 8² = 36 + 64 = 100, so c = 10 cm.

3. A right-angled triangle has legs of 20 cm and 21 cm. How long is the hypotenuse?

   1. A. 28 cm
   2. B. 29 cm ✓
   3. C. 1 cm
   4. D. 58 cm

   Answer: 29 cm. c² = 20² + 21² = 400 + 441 = 841, so c = 29 cm.

4. A right-angled triangle has legs of 3 cm and 4 cm. How long is the hypotenuse?

   1. A. 1 cm
   2. B. 10 cm
   3. C. 5 cm ✓
   4. D. 7 cm

   Answer: 5 cm. c² = 3² + 4² = 9 + 16 = 25, so c = 5 cm.

5. A right-angled triangle has legs of 10 cm and 24 cm. How long is the hypotenuse?

   1. A. 26 cm ✓
   2. B. 25 cm
   3. C. 34 cm
   4. D. 14 cm

   Answer: 26 cm. c² = 10² + 24² = 100 + 576 = 676, so c = 26 cm.

6. A right-angled triangle has legs of 5 cm and 12 cm. How long is the hypotenuse?

   1. A. 17 cm
   2. B. 7 cm
   3. C. 13 cm ✓
   4. D. 14 cm

   Answer: 13 cm. c² = 5² + 12² = 25 + 144 = 169, so c = 13 cm.

7. A right-angled triangle has legs of 14 cm and 48 cm. How long is the hypotenuse?

   1. A. 50 cm ✓
   2. B. 51 cm
   3. C. 62 cm
   4. D. 34 cm

   Answer: 50 cm. c² = 14² + 48² = 196 + 2304 = 2500, so c = 50 cm.

8. A right-angled triangle has legs of 16 cm and 30 cm. How long is the hypotenuse?

   1. A. 33 cm
   2. B. 34 cm ✓
   3. C. 35 cm
   4. D. 14 cm

   Answer: 34 cm. c² = 16² + 30² = 256 + 900 = 1156, so c = 34 cm.

9. A right-angled triangle has legs of 7 cm and 24 cm. How long is the hypotenuse?

   1. A. 25 cm ✓
   2. B. 50 cm
   3. C. 26 cm
   4. D. 31 cm

   Answer: 25 cm. c² = 7² + 24² = 49 + 576 = 625, so c = 25 cm.

10. A right-angled triangle has legs of 8 cm and 15 cm. How long is the hypotenuse?

    1. A. 17 cm ✓
    2. B. 18 cm
    3. C. 34 cm
    4. D. 16 cm

    Answer: 17 cm. c² = 8² + 15² = 64 + 225 = 289, so c = 17 cm.

11. A right-angled triangle has legs of 24 cm and 45 cm. How long is the hypotenuse?

    1. A. 51 cm ✓
    2. B. 69 cm
    3. C. 50 cm
    4. D. 21 cm

    Answer: 51 cm. c² = 24² + 45² = 576 + 2025 = 2601, so c = 51 cm.

12. A right-angled triangle has legs of 21 cm and 72 cm. How long is the hypotenuse?

    1. A. 74 cm
    2. B. 93 cm
    3. C. 76 cm
    4. D. 75 cm ✓

    Answer: 75 cm. c² = 21² + 72² = 441 + 5184 = 5625, so c = 75 cm.

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