Geometry

Question Analysis

This question is about applying the Triangle Inequality Theorem to determine the possible length of 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, the sum of the lengths of any two sides must be greater than the length of the third side. Mathematically, if , , and  are the side lengths of a triangle, then a + b>c, a + c>b, and b + c>a. This can also be expressed as |a - b|<c<a + b.

Step - by - Step Solution

Let  (length of ) and  (length of ).

First, calculate : .

Then, calculate :

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