Geometry

Question Analysis

This question is based on the Triangle Inequality Theorem, aiming to determine which set of lengths violates the theorem and thus cannot form a triangle.

Key Concept Explanation

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Mathematically, for side lengths , , and , we need a + b>c, a + c>b, and b + c>a.

Step - by - Step Solution

1. For the set :

18 + 26 = 44>42

18 + 42 = 60>26

26 + 42 = 68>18

All inequalities hold.

2. For the set

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