Geometry

Question Analysis

This question focuses on the relationship between the perimeters of similar triangles. Given the ratio of corresponding side lengths, the main task is to determine the ratio of their perimeters, leveraging the fundamental property of similar shapes.

Key Concept Explanation

For similar triangles, the ratio of the perimeters is identical to the ratio of the corresponding side lengths. Since the perimeter of a triangle is the sum of its side lengths, and corresponding sides of similar triangles maintain a constant ratio, the sum of these side lengths (the perimeter) will also be in 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 , , .

We know that .

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

Then, the ratio of the perimeters is

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