Geometry

Question Analysis

The main focus is to use the Triangle Inequality Theorem to determine the range of possible lengths 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 three inequalities must hold: a + b>c, a + c>b, and b + c>a. When two side lengths are known, we can find the range of the third side by using the inequalities|a - b|<c<a + b. Geometrically, this ensures that the three sides can be arranged to form a closed - loop shape.

Step - by - Step Solution

1. Let  and .

Calculate :

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