Geometry

Question Analysis

This question involves the Side - Splitter Theorem. The main focus is to use the proportional relationship established by a line parallel to one side of a triangle () to set up an equation and solve for the unknown variable .

 

Key Concept Explanation

The Side - Splitter Theorem 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 , since , we have .

 

Step - by - Step Solution

1. First, identify the known side lengths: , , and , .

2. According to the Side - Splitter Theorem, set up the proportion: .

3. Simplify the left - hand side of the proportion: . So the equation becomes

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