Geometry

Question Analysis

The main focus is to use the Triangle Inequality Theorem to find the smallest possible whole - number length for the third side of a triangle, given the lengths of the other two sides.

 

Key Concept Explanation

The Triangle Inequality Theorem states that for any triangle with side lengths , , and , the following three inequalities must hold: a + b>c, a + c>b, and b + c>a. When we know two side lengths and want to find the range of the third side, we use these inequalities to determine the possible values.

 

Step - by - Step Solution

1. Let the side lengths of the triangle be , , and  be the third side.

According to the Triangle Inequality Theorem, |a - b|<c<a + b.

First, calculate : .

And .

So, 4 < c < 18.

2. Since  must be a whole number greater than

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