Final answer:
The set of sides that form a right-angled triangle, according to the Pythagorean theorem, is option (C) 8 cm, 15 cm, 17 cm, as it satisfies the equation a² + b² = c².
Step-by-step explanation:
To determine which set of side lengths correspond to a right-angled triangle, we can use the Pythagorean theorem, which states that for a right triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This relationship is given by the equation a² + b² = c², where c represents the length of the hypotenuse and a and b are the lengths of the other two sides.
Let's evaluate each set of lengths:
- (A) 3 cm, 4 cm, 6 cm: 3² + 4² ≠ 6² (9 + 16 ≠ 36)
- (B) 6 cm, 8 cm, 12 cm: 6² + 8² ≠ 12² (36 + 64 ≠ 144)
- (C) 8 cm, 15 cm, 17 cm: 8² + 15² = 17² (64 + 225 = 289)
- (D) 9 cm, 12 cm, 13 cm: 9² + 12² ≠ 13² (81 + 144 ≠ 169)
Therefore, the sides that form a right-angled triangle are 8 cm, 15 cm, 17 cm, which makes option (C) the correct choice.