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 lengths of  and , and then set up the proportion to solve for .

 

Step - by - Step Solution

1. Find the length of :

Given  and , we can find  by subtracting  from , so .

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

We know