Question

Which are the possible side lengths of a triangle?

3 cm, 5 cm, 9 cm
4 cm, 8 cm, 10 cm
6 cm, 9 cm, 17 cm
8 cm, 10 cm, 18 cm

Answer 1

A set of three lengths forms a (non-degenerate) triangle iff the sum of any two sides is strictly greater than the third.

Check each:
- 3, 5, 9: 3 + 5 = 8 ≤ 9 → no.
- 4, 8, 10: 4 + 8 = 12 > 10, 4 + 10 = 14 > 8, 8 + 10 = 18 > 4 → yes.
- 6, 9, 17: 6 + 9 = 15 ≤ 17 → no.
- 8, 10, 18: 8 + 10 = 18 = 18 → degenerate (not a triangle).

So only 4 cm, 8 cm, 10 cm can be the side lengths of a triangle.