Geometry

Question Analysis

This question focuses on applying the concept of similar shapes, specifically on determining the ratio of the perimeters of two similar triangles given the ratio of their corresponding side lengths.

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, and if each side of one triangle is in a certain ratio to the corresponding side of a similar triangle, the sum of all sides (the perimeter) will 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 , , .

Given that .

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

Then

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