Geometry

Question Analysis

This question involves the Perimeters of Similar Shapes. The main focus is on using the property that for similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding side lengths to find the required ratio.

Key Concept Explanation

For similar triangles, if the scale factor (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 a consistent proportionality for all linear aspects.

Step - by - Step Solution

1. Identify corresponding sides and find the ratio of one pair of corresponding sides. Let's take  and .

Calculate the ratio: .

We can verify with another pair. For example, take  and ,

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