Geometry

Question Analysis

The main focus is to use the Triangle Inequality Theorem to determine the upper bound of the length of 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 three inequalities must hold: a + b>c, a + c>b, and b + c>a. When two side lengths are known, the inequality c < a + b helps us find the maximum possible value of the third side.

 

Step - by - Step Solution

1. Let and . According to the Triangle Inequality Theorem, for the third side , we have c < a + b.

Calculate : .

Also, , so the range of is 5 < c < 21.

2. Since

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