Geometry

Question Analysis

The core objective is to apply the Triangle Inequality Theorem to figure out which of the given values could represent the length of side in , considering the known lengths of sides and .

Key Concept Explanation

The Triangle Inequality Theorem posits 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 feasible range of the third side.

Step - by - Step Solution

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

Calculate : .

Calculate :

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