Geometry

Question Analysis

This question applies the Side - splitter theorem corollary. Given that in , we can use the proportional relationship of the sides divided by the parallel line to find the length of . The key is to correctly identify and set up the proportion using the known side lengths.

 

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 .

 

Step - by - Step Solution

1. First, identify the known values:

, , and .

2. Then, set up the proportion according to the Side - splitter theorem corollary:

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