Question

Which set of side lengths is a Pythagorean triple?
2, 3, 13
5, 7, 12
10, 24, 29
11, 60, 61

Answer 1

Check each set using a^2 + b^2 = c^2 (with c the largest side):

- 2, 3, 13: 2^2 + 3^2 = 4 + 9 = 13 ≠ 13^2 (169) → not a triple.
- 5, 7, 12: 5^2 + 7^2 = 25 + 49 = 74 ≠ 12^2 (144) → not a triple.
- 10, 24, 29: 10^2 + 24^2 = 100 + 576 = 676 ≠ 29^2 (841) → not a triple.
- 11, 60, 61: 11^2 + 60^2 = 121 + 3600 = 3721 = 61^2 → this is a Pythagorean triple.

So only 11, 60, 61 is a Pythagorean triple.