Geometry

Question Analysis

This question involves the Side - Splitter Theorem. The main focus is to use the proportional relationship created by a line parallel to one side of a triangle () to find the unknown side length .

 

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 . First, we need to find the length of using the given length of , and then set up the proportion to solve for .

 

Step - by - Step Solution

1. Find the length of :

Given , let , then .

2. Set up the proportion using the Side - Splitter Theorem:

We know , , and . According to the theorem,

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