Geometry

Question Analysis

The focus is applying the Side - splitter theorem corollary. Since , we can use the proportional relationship of the sides divided by the parallel line to find the length of . We need to use the known side lengths , , and .

 

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 , we have .

 

Step - by - Step Solution

1. First, find : .

2. Set up the proportion: , substituting values gives

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