Question

Which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle?

8, 10, 14
9, 12, 15
10, 14, 17
12, 15, 19

Answer 1

A triangle is obtuse if, with sides a ≤ b ≤ c, we have c^2 > a^2 + b^2.

Check each:
- 8, 10, 14: 14^2 = 196, 8^2+10^2 = 64+100 = 164 → 196 > 164, obtuse.
- 9, 12, 15: 15^2 = 225, 9^2+12^2 = 81+144 = 225 → right triangle.
- 10, 14, 17: 17^2 = 289, 10^2+14^2 = 100+196 = 296 → acute.
- 12, 15, 19: 19^2 = 361, 12^2+15^2 = 144+225 = 369 → acute.

So 8, 10, 14.