Geometry

Question Analysis

This question focuses on applying the Triangle Angle Bisector Theorem. Given that  is the angle bisector of  in , along with the lengths of  and , and the length of , we need to find the length of . The key is to use the proportional relationship established by the theorem.

 

Key Concept Explanation

The Triangle Angle Bisector Theorem states that if a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the other two sides. In , since  bisects , we have .

 

Step - by - Step Solution

1. First, identify the given values: , , and . Let , then .

2. Then, apply the Triangle Angle Bisector Theorem proportion .

Substitute the known values into the proportion: .

3. Cross - multiply: .

Expand the left - hand side:

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