Geometry

Question Analysis

The main focus is to use the Triangle Inequality Theorem to determine the largest possible 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 , the following inequalities must hold: a + b>c, a + c>b, and b + c>a. When two side lengths are known, these inequalities help in establishing the range of values for the third side.

 

Step - by - Step Solution

1. Let  and , and  be the third side.

According to the theorem, c < a + b. Also, |a - b| < c. Here,  and . So the range for  is 3 < c < 13.

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

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