Geometry

Question Analysis

The main focus is applying 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 . We need to correctly set up the proportion using 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  with , we have .

 

Step - by - Step Solution

1. First, identify the known values:

, , and