Geometry

Question Analysis

The main focus is to find the perimeter of the smaller polygon using the side - length ratio of two similar polygons and the perimeter of the larger polygon. Since the ratio of perimeters of similar polygons is equal to the ratio of their corresponding side lengths, we can set up a proportion to solve for the unknown perimeter.

Key Concept Explanation

For similar polygons, if the ratio of corresponding 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 . Given the side - length ratio , the ratio of perimeters is also . So we have the proportion

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