Question

Which of the following list of side lengths could form a triangle?

4, 5, and 6
5, 6, and 12
10, 12, and 25
2, 2, and 4

Answer 1

Use the triangle inequality: for three side lengths a, b, c to form a (nondegenerate) triangle, each pair must sum to more than the third.

Check each set:
- 4, 5, 6: 4+5=9>6, 4+6=10>5, 5+6=11>4 → yes, forms a triangle.
- 5, 6, 12: 5+6=11 ≤ 12 → no.
- 10, 12, 25: 10+12=22 ≤ 25 → no.
- 2, 2, 4: 2+2=4 = 4 (degenerate) → not a triangle.

So only 4, 5, and 6 can form a triangle.