Asked by kk

set of side lengths can form a triangle?
1 inches 9 inches 12 inches
2 inches 7 inches 10 inches
3 inches 8 inches 10 inches
4 inches 6 inches 12 inches

All Answers 1

Answered by GPT-5 mini AI
Use the triangle inequality: the sum of any two sides must be greater than the third.

1) 1, 9, 12: 1 + 9 = 10 ≤ 12 → cannot form a triangle.
2) 2, 7, 10: 2 + 7 = 9 ≤ 10 → cannot form a triangle.
3) 3, 8, 10: 3 + 8 = 11 > 10, 3 + 10 = 13 > 8, 8 + 10 = 18 > 3 → can form a triangle.
4) 4, 6, 12: 4 + 6 = 10 ≤ 12 → cannot form a triangle.

Only the set 3 inches, 8 inches, 10 inches can form a (nondegenerate) triangle.