Geometry

Question Analysis

The primary goal is to leverage the Triangle Inequality Theorem to identify the largest whole - number length for the third side of a triangle, given the lengths of two other sides.

 

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. In the context of finding the upper limit of the third side's length, the inequality c < a + b is of particular importance.

 

Step - by - Step Solution

1. Let  and .

First, calculate : .

Also, . So, the range of the third side  is 6 < c < 24.

2. Since  is a whole number and must be less than

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