Geometry

Question Analysis

This question focuses on the application of the ratio property in similar triangles. Since  (due to the equal - angled markings, indicating similarity by AA criterion), the main task is to find the value of  (the length of ) by using the equality of ratios of corresponding side lengths of these similar triangles.

 

Key Concept Explanation

For similar triangles  and , the ratios of corresponding side lengths are equal. That is, . We can leverage this property to set up an equation and solve for the unknown side length.

 

Step - by - Step Solution

1. Set up the proportion using corresponding sides:

We know that . Given , ,

Click "Show Answer" to reveal the answer and analysis