Question

Which set of side lengths do not form a triangle?

2,3,5
3,5,7
5,7,10
6,14,18

Answer 1

Use the triangle inequality (sum of any two sides must be greater than the third).

- 2+3 = 5, so 2, 3, 5 fail (degenerate; do not form a triangle).
- 3,5,7: all pairwise sums exceed the third → forms a triangle.
- 5,7,10: all pairwise sums exceed the third → forms a triangle.
- 6,14,18: all pairwise sums exceed the third → forms a triangle.

So 2, 3, 5 do not form a triangle.