Geometry

Question Analysis

This question is about applying the Side - splitter theorem corollary. Since , we can establish a proportion using the segments of the sides of to find the length of . The key is to correctly identify the corresponding segments divided by the parallel line.

 

Key Concept Explanation

The Side - splitter theorem corollary 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 with , we have . Also, we know that .

 

Step - by - Step Solution

1. First, identify the known values:

, , and .

2. Set up the proportion according to the Side - splitter theorem corollary:

. Substituting the known values, we get .

3. Cross - multiply:

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