Geometry

Question Analysis

This question focuses on the Perimeters of Similar Shapes. The main task is to use the fact that for similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding side lengths to find the required ratio.

Key Concept Explanation

For similar triangles, if the ratio of corresponding side lengths is , then the ratio of their perimeters is also . This is because perimeter is a linear measurement, and similar triangles maintain a consistent proportionality for all linear dimensions.

Step - by - Step Solution

1. First, find the ratio of corresponding side lengths. Let's take the side of length in the left triangle and the side of length in the right triangle.

Calculate the ratio: .

We can also check with the other pair of corresponding sides. Let's take the side of length in the left triangle. Suppose the corresponding side in the right triangle is . Since the triangles are similar,

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