Geometry

Question Analysis

This question focuses on the application of Ratio in Similar Shapes. The core task is to utilize the fact that corresponding sides of similar triangles are in proportion. Given the lengths of two sides of one triangle and one side of a similar triangle, we need to determine the missing side length by establishing and solving a proportion equation.

 

Key Concept Explanation

In the context of similar triangles, the fundamental principle is that the ratios of corresponding side lengths are equal. This property allows us to set up an equation (a proportion) to find unknown side lengths. By correctly matching the corresponding sides of the similar triangles, we can use cross - multiplication and basic algebraic operations to solve for the missing side.

 

Step - by - Step Solution

1. Set up the proportion:

Since the triangles are similar, and 6 corresponds to 4, and 4.2 corresponds to , we can set up the proportion .

2. Cross - multiply:

Cross - multiplying gives us .

3. Calculate the right - hand side:

First, find . So the equation becomes

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