Geometry

Question Analysis

This question tests the understanding of the Triangle Inequality Theorem. The main focus is to check if the given side lengths satisfy the conditions of the theorem to 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. That is, for side lengths , , and , we must have a + b>c, a + c>b, and b + c>a.

Step - by - Step Solution

1. For the set :

13 + 21 = 34>31

13 + 31 = 44>21

21 + 31 = 52>13

All inequalities hold.

2. For the set

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