Geometry

Question Analysis

This question involves the Side - Splitter Theorem. The main focus is to apply the theorem, which states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally, to find the unknown side length .

 

Key Concept Explanation

The Side - Splitter Theorem: In , since , we have . Also, the ratios of the lengths of the parallel lines and the corresponding sides of the triangles are related. That is, .

 

Step - by - Step Solution

1. First, find the length of : .

2. According to the Side - Splitter Theorem , substitute the known values ,

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