Geometry

Question Analysis

The focus is applying the Side - splitter theorem corollary. Given , we use the proportional relationship of sides divided by the parallel line to find with known 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. So, in , we have .

 

Step - by - Step Solution

1. First, find : .

2. Set up the proportion: