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 find the ratio of their perimeters.

Key Concept Explanation

For similar triangles, if the ratio of corresponding side lengths is , then the ratio of their perimeters is the same as the ratio of their corresponding side lengths. This is because the perimeter of a triangle is the sum of its side lengths, and when each side of one triangle is in the ratio  with the corresponding side of a similar triangle, the sum of the side lengths (perimeter) 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 .

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