Geometry

Question Analysis

This question focuses on using the property of equal ratios of corresponding sides in similar right - angled triangles. The main task is to find the unknown side length  by setting up and solving a proportion based on the known side lengths of the two similar triangles.

Key Concept Explanation

For similar triangles, the ratios of corresponding side lengths are equal. That is, if  and  are similar, then . We can use this principle to establish an equation and solve for the unknown side.

Step - by - Step Solution

1. Set up the proportion:

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

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