Geometry

Question Analysis

This question focuses on the Perimeters of Similar Shapes. The core is to use the property that for similar triangles, the ratio of their perimeters is the same as the ratio of their corresponding side lengths to find the required ratio.

Key Concept Explanation

For similar triangles, if the ratio of corresponding side lengths is , then the ratio of their perimeters is also . This is because perimeter is a linear measurement, and similar triangles maintain consistent proportionality for linear aspects.

Step - by - Step Solution

1. Identify a pair of corresponding sides. Let's take the side of length  in the left triangle and the side of length  in the right triangle.

2. Calculate the ratio: .

We can verify with another pair. Taking the side of length  in the left triangle, if the corresponding side in the right triangle is