Geometry

Question Analysis

This question is about applying the Side - Splitter Theorem. The key is to use the proportional relationship formed by the parallel line to in . First, we need to find the length of using the given lengths of and , and then set up a proportion to find .

 

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 based on the Side - Splitter Theorem:

We know ,

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