In the following sets, which set represents the sides of a right-angled triangle?

Question

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To determine if a set of three sides can form a right-angled triangle, we use the Pythagoras theorem: a² + b² = c², where c is the longest side.

1. For {5, 10, 12}:
   - Longest side = 12
   - Check: 5² + 10² = 25 + 100 = 125
   - 12² = 144
   - 125 ≠ 144, so not right-angled.

2. For {3, 4, 6}:
   - Longest side = 6
   - Check: 3² + 4² = 9 + 16 = 25
   - 6² = 36
   - 25 ≠ 36, so not right-angled.

3. For {5, 12, 13}:
   - Longest side = 13
   - Check: 5² + 12² = 25 + 144 = 169
   - 13² = 169
   - 169 = 169, so it is a right-angled triangle.

4. For {8, 15, 16}:
   - Longest side = 16
   - Check: 8² + 15² = 64 + 225 = 289
   - 16² = 256
   - 289 ≠ 256, so not right-angled.

Hence, only the set {5, 12, 13} represents the sides of a right-angled triangle.

Answer

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