Question

Charla has six segments with which to make two triangles. The segments lengths are 2 in., 3 in., 4 in., 5 in., 6 in., and 7 in. Which are possible side lengths of her two triangles?

2 in., 4 in., 6 in. and 3 in., 5 in., 7 in.
2 in., 5 in., 6 in. and 3 in., 4 in., 7 in.
2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.
2 in., 3 in., 6 in. and 4 in., 5 in., 7 in.

Answer 1

Only 2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.

Check triangle inequality (sum of two smaller sides > largest):
- 2,4,6: 2+4 = 6 (degenerate) — no
- 3,5,7: 3+5 = 8 > 7 — yes
- 2,5,6: 2+5 = 7 > 6 — yes
- 3,4,7: 3+4 = 7 (degenerate) — no
- 2,3,4: 2+3 = 5 > 4 — yes
- 5,6,7: 5+6 = 11 > 7 — yes
- 2,3,6: 2+3 = 5 < 6 — no
- 4,5,7: 4+5 = 9 > 7 — yes

Only 2,3,4 and 5,6,7 both satisfy the strict triangle inequalities.