Geometry

Question Analysis

This question focuses on applying the SSS (Side - Side - Side) Triangle Similarity Theorem. Given that , the main task is to find the value of  by using the property that the ratios of corresponding side lengths in similar triangles are equal.

 

Key Concept Explanation

The SSS Triangle Similarity Theorem states that if the ratios of the lengths of the corresponding sides of two triangles are equal, then the two triangles are similar. For similar triangles, we can set up equations based on these equal side - length ratios to solve for unknown variables.

 

Step - by - Step Solution

1. Set up the ratio equation based on corresponding sides:

Since , we have .

Here, , , , and .

So the equation becomes