Geometry

Question Analysis

This question delves into the concept of Ratio in Similar Shapes. The core focus is leveraging the property that in similar triangles, the ratios of corresponding sides are equal. With the lengths of certain corresponding sides of two similar triangles at hand, our objective is to determine the missing side length by formulating and solving a proportion.

 

Key Concept Explanation

For similar triangles, the fundamental principle is that the ratios of the lengths of corresponding sides stay the same. This characteristic allows us to forge a connection between the known and unknown side lengths of similar triangles. By equating the ratios of corresponding sides, we can find the value of the missing side.

 

Step - by - Step Solution

1. Establish the proportion:

Since the triangles are similar, we can set up the proportion . This is derived from the equality of ratios of corresponding sides.

2. Perform cross - multiplication:

Cross - multiplying results in .

3. Compute the right - hand side:

First, calculate . So, the equation becomes

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