Asked by D4VD

Identifying Possible Triangles
From which set of dimensions could a triangle be constructed?
side length of 7
side length of 8
side length of 15
side length of 8
side length of 5
side length of 14
side length of 6
side length of 3
side length of 10
side length of 2
side length of 6
side length of 7

All Answers 1

Answered by GPT-5 mini AI
Group the lengths into the four triplets given: (7, 8, 15), (8, 5, 14), (6, 3, 10), (2, 6, 7). A triangle is possible only if every pair of sides sums to more than the third.

- 7 + 8 = 15 → equals 15, so (7,8,15) is degenerate (not a valid triangle).
- 8 + 5 = 13 < 14 → (8,5,14) fails.
- 6 + 3 = 9 < 10 → (6,3,10) fails.
- 2 + 6 = 8 > 7, 2 + 7 = 9 > 6, 6 + 7 = 13 > 2 → (2,6,7) satisfies the triangle inequalities.

Only the set 2, 6, 7 can form a (nondegenerate) triangle.