Geometry

Question Analysis

The key is to use the property that for similar polygons, the ratio of their perimeters is equal to the ratio of their corresponding side lengths. We know the ratio of side lengths and the perimeter of the larger polygon, and we need to find the perimeter of the smaller polygon.

Key Concept Explanation

For similar polygons, if the ratio of side lengths is , then the ratio of their perimeters  and  is also , i.e., .

Step - by - Step Solution

1. Set up the proportion:

Let the perimeter of the smaller polygon be . The ratio of side lengths is , so the ratio of perimeters is also . We can set up the proportion

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