Geometry

Question Analysis

This question focuses on using the property of ratios in similar shapes. The main task is to find the unknown side length of a similar triangle by leveraging the fact that the ratios of corresponding side lengths in similar triangles are equal.

Key Concept Explanation

For similar triangles, the ratios of corresponding side lengths are constant. If and are similar, then . We can use this equal - ratio relationship to set up an equation and solve for the unknown side.

Step - by - Step Solution

1. Set up the proportion:

We can take the ratio of the first pair of corresponding sides and the third pair of corresponding sides . Since the ratios of corresponding sides in similar triangles are equal, we have the proportion .

2. Solve the proportion for :

Cross - multiply the proportion:

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