Geometry

Question Analysis

The central goal is to employ the Triangle Inequality Theorem to identify which of the given values could represent the length of side in , considering the lengths of sides and .

Key Concept Explanation

The Triangle Inequality Theorem states that for any triangle with side lengths , , and , three inequalities must hold: a + b>c, a + c>b, and b + c>a. When two side lengths are provided, we can use the inequalities |a - b|<c<a + b to determine the range of possible lengths for the third side. This theorem is rooted in the geometric principle that the shortest path between two points is a straight line.

Step - by - Step Solution

1. Let (length of ) and (length of ).

Calculate : .

Calculate :

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