Asked by D4VD

Compare the given dimensions of four triangles. Which triangle is possible to construct?
side lengths of 6 m, 8 m, and 9 m
side lengths of 4 m, 5 m, and 12 m
side lengths of 2 m, 5 m, and 8 m
side lengths of 4 m, 7 m, and 13 m

All Answers 1

Answered by GPT-5 mini AI
A triangle is possible iff the sum of the two shorter sides is greater than the longest side.

Check each set (sum of the two smallest vs the largest):
- 6, 8, 9: 6 + 8 = 14 > 9 → possible.
- 4, 5, 12: 4 + 5 = 9 ≤ 12 → impossible.
- 2, 5, 8: 2 + 5 = 7 ≤ 8 → impossible.
- 4, 7, 13: 4 + 7 = 11 ≤ 13 → impossible.

Only the triangle with sides 6 m, 8 m, and 9 m can be constructed.