Pythagoras Theorem Worksheet

Name: ____________________________
Class: ____________________________
Date: ____________________________

Formula

For a right-angled triangle:

a² + b² = c²

where c is the hypotenuse (the side opposite the right angle).

A. Find the Hypotenuse

1. The two shorter sides are 3 cm and 4 cm. Find the hypotenuse.
2. The two shorter sides are 5 cm and 12 cm. Find the hypotenuse.
3. The two shorter sides are 6 cm and 8 cm. Find the hypotenuse.
4. The two shorter sides are 8 cm and 15 cm. Find the hypotenuse.
5. The two shorter sides are 7 cm and 24 cm. Find the hypotenuse.
6. The two shorter sides are 9 cm and 12 cm. Find the hypotenuse.
7. The two shorter sides are 12 cm and 16 cm. Find the hypotenuse.
8. The two shorter sides are 10 cm and 24 cm. Find the hypotenuse.
9. The two shorter sides are 20 cm and 21 cm. Find the hypotenuse.
10. The two shorter sides are 12 cm and 35 cm. Find the hypotenuse.

B. Find the Missing Side

11. Hypotenuse = 5 cm, one side = 3 cm. Find the other side.
12. Hypotenuse = 13 cm, one side = 5 cm. Find the other side.
13. Hypotenuse = 10 cm, one side = 6 cm. Find the other side.
14. Hypotenuse = 17 cm, one side = 8 cm. Find the other side.
15. Hypotenuse = 25 cm, one side = 7 cm. Find the other side.
16. Hypotenuse = 15 cm, one side = 9 cm. Find the other side.
17. Hypotenuse = 20 cm, one side = 12 cm. Find the other side.
18. Hypotenuse = 29 cm, one side = 20 cm. Find the other side.
19. Hypotenuse = 26 cm, one side = 10 cm. Find the other side.
20. Hypotenuse = 41 cm, one side = 9 cm. Find the other side.

C. Choose the Correct Answer

21. Which formula represents the Pythagorean theorem?
    a) a + b = c
    b) a² + b² = c²
    c) a² − b² = c²
    d) 2a + 2b = c
22. In a right triangle, the longest side is called the:
    a) base
    b) altitude
    c) hypotenuse
    d) radius
23. If a = 6 and b = 8, then c is:
    a) 9
    b) 10
    c) 12
    d) 14
24. If the hypotenuse is 13 cm and one leg is 12 cm, the other leg is:
    a) 3 cm
    b) 4 cm
    c) 5 cm
    d) 6 cm
25. The Pythagorean theorem applies to:
    a) all triangles
    b) equilateral triangles only
    c) right-angled triangles
    d) circles

D. True or False

26. The hypotenuse is always the longest side of a right triangle. __________
27. The Pythagorean theorem can be used for any triangle. __________
28. For sides 3 cm, 4 cm, and 5 cm, the triangle is right-angled. __________
29. If a² + b² = c², then c is the hypotenuse. __________
30. A right triangle can have two right angles. __________

E. Word Problems

31. A ladder is 10 m long and reaches a wall 8 m above the ground. How far is the foot of the ladder from the wall?
32. A rectangular field is 15 m long and 20 m wide. Find the length of its diagonal.
33. A television screen is 24 cm wide and 18 cm high. Find its diagonal length.
34. A person walks 9 km east and then 12 km north. How far is the person from the starting point?
35. A ramp is 13 m long and rises 5 m vertically. Find the horizontal distance covered by the ramp.
36. A rectangular garden measures 12 m by 16 m. Find the distance from one corner to the opposite corner.
37. A kite string is 25 m long. The kite is 24 m above the ground. How far is the person holding the string from the point directly below the kite?
38. A right-angled triangular sign has perpendicular sides of 9 cm and 40 cm. Find the length of its longest side.
39. A boat travels 15 km south and then 20 km east. How far is it from its starting point?
40. A square has a side length of 10 cm. Find the length of its diagonal.

F. Challenge Questions

41. The sides of a triangle are 9 cm, 40 cm, and 41 cm. Is it a right-angled triangle? Show your calculation.
42. The sides of a triangle are 8 cm, 15 cm, and 17 cm. Verify whether it is a right triangle.
43. A right triangle has a hypotenuse of 50 cm and one leg of 14 cm. Find the other leg.
44. A right triangle has one leg of 16 cm and a hypotenuse of 34 cm. Find the missing leg.
45. A rectangular room is 21 m long and 28 m wide. Find the diagonal distance across the room.

Total Questions: 45

Teacher’s Signature: ____________________________

Answer Key — Pythagoras Theorem Worksheet

A. Find the Hypotenuse

1. 5 cm
2. 13 cm
3. 10 cm
4. 17 cm
5. 25 cm
6. 15 cm
7. 20 cm
8. 26 cm
9. 29 cm
10. 37 cm

B. Find the Missing Side

11. 4 cm
12. 12 cm
13. 8 cm
14. 15 cm
15. 24 cm
16. 12 cm
17. 16 cm
18. 21 cm
19. 24 cm
20. 40 cm

C. Choose the Correct Answer

21. b) a² + b² = c²
22. c) hypotenuse
23. b) 10
24. c) 5 cm
25. c) right-angled triangles

D. True or False

26. True
27. False
28. True
29. True
30. False

E. Word Problems

31. 6 m
32. 25 m
33. 30 cm
34. 15 km
35. 12 m
36. 20 m
37. 7 m
38. 41 cm
39. 25 km
40. 10√2 cm (approximately 14.14 cm)

F. Challenge Questions

41. Yes.
    9² + 40² = 81 + 1600 = 1681 = 41²
42. Yes.
    8² + 15² = 64 + 225 = 289 = 17²
43. 48 cm
44. 30 cm
45. 35 m