Triangle inequality test — pick the set that cannot form a triangle: The lengths (in cm) of three line segments are given. Which set cannot be the sides of a triangle?

Introduction / Context:Triangle inequality demands that the sum of any two sides be strictly greater than the third for all three comparisons.

Given Data / Assumptions:We check each option against the triangle inequality.

Concept / Approach:For each triplet (a, b, c), verify: a + b > c, b + c > a, and c + a > b. Equality is insufficient.

Step-by-Step Solution:(2,3,4): 2+3=5>4 ✓(2,3,5): 2+3=5 = 5 → not strictly greater ✗(2,4,5): sums all strictly greater ✓(3,4,5): classic Pythagorean triple ✓

Verification / Alternative check:Only option (2,3,5) fails strict inequality once; hence it cannot form a triangle.

Why Other Options Are Wrong:They satisfy all strict inequalities.

Common Pitfalls:Accepting equality; triangles require strict inequality.

Final Answer:2, 3, 5