Geometry

Question Analysis

The main focus is to apply the Triangle Inequality Theorem to figure out the range of possible lengths for the third side of a triangle, given the lengths of two sides.

Key Concept Explanation

The Triangle Inequality Theorem states that for any triangle with side lengths , , and , the inequalities a + b>c, a + c>b, and b + c>a must hold. When two side lengths  and  are known, we can find the range of the third side  using |a - b|<c<a + b. This ensures that the three sides can connect to form a triangle.

Step - by - Step Solution

1. Let  and .

Calculate :

.

Calculate

Click "Show Answer" to reveal the answer and analysis