Geometry

Question Analysis

This question focuses on applying the principle of similar shapes to find the ratio of the perimeters of two similar triangles. Given the ratio of their corresponding side lengths, the key is to use the relationship between side - length ratios and perimeter ratios in 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 ratio , then the sum of these side lengths (the perimeters) will also be in the 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

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