PYTHAGORAS THEOREM REVISION QUESTIONS WITH ANSWERS

Pythagoras' Theorem Questions

1. State Pythagoras’ Theorem.

2. In a right-angled triangle, \(a = 3\), \(b = 4\). Find the hypotenuse \(c\).

3. If \(c = 13\) and \(a = 5\), find \(b\).

4. Determine if the triangle with sides 5, 12, and 13 is a right triangle.

5. A ladder leans against a wall. It is 10 m long and reaches 8 m up the wall. How far is the base from the wall?

6. Find the length of the diagonal of a rectangle 6 m long and 8 m wide.

7. The legs of a right triangle are equal. If the hypotenuse is 10 cm, find the length of each leg.

8. Can a triangle with sides 7 cm, 24 cm, and 25 cm be a right-angled triangle?

9. A triangle has sides 9 cm, 40 cm, and 41 cm. Is it a right triangle?

10. What is the hypotenuse of a right triangle with legs 8.5 cm and 6.5 cm?

11. Prove that a triangle with sides 6 cm, 8 cm, and 10 cm is a right triangle.

12. A right triangle has a hypotenuse of 15 cm and one leg 9 cm. Find the other leg.

13. A square has a diagonal of 10 cm. Find the length of one side.

14. Find the missing side: \(c = 17\), \(b = 8\). Find \(a\).

15. If a right triangle has legs 12 and 16, find the hypotenuse.

16. The diagonal of a square measures \( \sqrt{50} \) cm. What is the side length?

17. A triangle has sides 15 cm, 20 cm, and 25 cm. Is it a right triangle?

18. If \(a = 9\) and \(c = 15\), find \(b\).

19. Find the missing side of a triangle where \(a = 11\), \(b = 60\).

20. A square playground has a diagonal of 14.14 m. What is the length of one side?

21. Determine if sides 10 cm, 24 cm, and 26 cm form a right triangle.

22. In a right triangle, if one leg is 7 cm and the hypotenuse is 25 cm, find the other leg.

23. A triangle has sides 8 cm, 15 cm, and 17 cm. Is it right-angled?

24. The base of a ladder is 9 m away from the wall. It reaches 12 m up. How long is the ladder?

25. Find the hypotenuse of a triangle with sides \(a = 1.5\), \(b = 2.5\).

26. A triangle has legs 5 cm and 12 cm. Find the hypotenuse.

27. If the hypotenuse is 50 cm and one leg is 14 cm, find the other leg.

28. Prove that triangle with sides 9, 12, and 15 is right-angled.

29. Find the hypotenuse of triangle with legs \(a = 2\sqrt{2}\), \(b = 2\sqrt{3}\).

30. What type of triangle has sides 6 cm, 8 cm, and 10 cm?

Answers

1. In a right-angled triangle, \(c^2 = a^2 + b^2\).
2. \(c = 5\)
3. \(b = 12\)
4. Yes, \(13^2 = 5^2 + 12^2\)
5. \( \sqrt{100 - 64} = 6 \) m
6. \( \sqrt{36 + 64} = 10 \) m
7. \(x^2 + x^2 = 100 \Rightarrow x = \sqrt{50} \approx 7.07\) cm
8. Yes, \(49 + 576 = 625\), and \(25^2 = 625\)
9. Yes, \(81 + 1600 = 1681 = 41^2\)
10. \(c = \sqrt{72.25 + 42.25} = \sqrt{114.5} \approx 10.7\) cm
11. \(6^2 + 8^2 = 100 = 10^2\), hence right-angled
12. \(b = \sqrt{225 - 81} = \sqrt{144} = 12\) cm
13. \(x = \sqrt{100/2} = \sqrt{50} \approx 7.07\) cm
14. \(a = \sqrt{289 - 64} = \sqrt{225} = 15\)
15. \(c = \sqrt{144 + 256} = \sqrt{400} = 20\)
16. \(x = \sqrt{50/2} = \sqrt{25} = 5\) cm
17. \(15^2 + 20^2 = 625 = 25^2\), so yes
18. \(b = \sqrt{225 - 81} = \sqrt{144} = 12\)
19. \(c = \sqrt{121 + 3600} = \sqrt{3721} = 61\)
20. \(\sqrt{200} = 14.14\), so side = 10 m
21. \(100 + 576 = 676 = 26^2\), so yes
22. \(\sqrt{625 - 49} = \sqrt{576} = 24\)
23. \(64 + 225 = 289 = 17^2\), so yes
24. \(\sqrt{81 + 144} = \sqrt{225} = 15\) m
25. \(c = \sqrt{2.25 + 6.25} = \sqrt{8.5} \approx 2.92\)
26. \(c = \sqrt{25 + 144} = \sqrt{169} = 13\)
27. \(\sqrt{2500 - 196} = \sqrt{2304} = 48\)
28. \(9^2 + 12^2 = 225 = 15^2\), hence right-angled
29. \(c = \sqrt{8 + 12} = \sqrt{20} \approx 4.47\)
30. Right-angled triangle