Geometry

Question Analysis

This question focuses on the Perimeters of Similar Shapes. The key is to utilize the property that for similar triangles, the ratio of their perimeters is equivalent to the ratio of their corresponding side lengths to determine the required ratio.

Key Concept Explanation

For similar triangles, if the scale factor (the ratio of corresponding side lengths) is , then the ratio of their perimeters is also . This is because perimeter, being a linear measurement, adheres to the consistent proportionality maintained by similar triangles for all linear dimensions.

Step - by - Step Solution

1. First, identify a pair of corresponding sides. Let's take and .

Calculate the ratio: .

Verify with another pair. For and ,

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