Geometry

Question Analysis

The main focus is to use the Triangle Inequality Theorem to determine which of the given values could be the length of side in , given 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 known, we can use the inequalities |a - b|<c<a + b to find the range of possible lengths for the third side. This theorem is based on 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 :