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.

Key Concept Explanation

For similar triangles, the ratio of the perimeters is equal to the ratio of the corresponding side lengths. Since the perimeter of a triangle is the sum of its side lengths, and each side of one triangle is in a fixed ratio to the corresponding side of a similar triangle, the sum of these side lengths (the perimeter) 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 , , .

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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