Geometry

Question Analysis

This question focuses on applying the Side - splitter theorem corollary. Given that in , we need to use the correct proportional relationship of the sides divided by the parallel line to find the length of . The key is to accurately set up the proportion using the known side lengths.

 

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. In with , the correct proportion should be . But we want to find , and since , we can also set up the proportion . First, we find .

 

Step - by - Step Solution

1. First, identify the known values:

(calculated as

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