Geometry

Question Analysis

This question involves applying the Side - Splitter Theorem. The key is to utilize the proportional relationship formed by the parallel line  to  in . We'll first determine the length of , then set up the correct proportion based on the theorem to find the unknown side length .

 

Key Concept Explanation

The Side - Splitter Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally. In , since , we have .

 

Step - by - Step Solution

1. Find the length of :

Given  and , we can find  by subtracting  from , so .

2. Set up the proportion and solve for

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