Geometry

Question Analysis

This question focuses on applying the property of similar shapes to find the ratio of the perimeters of two similar triangles. Given the ratio of their corresponding side lengths, the core task is to determine the ratio of their perimeters using the fundamental relationship between similar triangles.

Key Concept Explanation

For similar triangles, the ratio of the perimeters is equal to the ratio of the corresponding side lengths. This is because the perimeter of a triangle is the sum of its side lengths. If the side lengths of two similar triangles are in a fixed ratio, then the sum of these side lengths (i.e., the perimeters) will maintain the same ratio.

Step - by - Step Solution

1. Let the side lengths of the first triangle be , ,  and the side lengths of the second triangle be , , .

Given that .

2. The perimeter of the first triangle , and the perimeter of the second triangle .

Then, the ratio of the perimeters

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