Geometry

Question Analysis  

The main focus is to find the length of the longest side of the larger polygon using the perimeter ratio of two similar polygons and the length of the longest side of the smaller polygon. The key is leveraging the fact that the ratio of corresponding side lengths of similar polygons is equal to their perimeter ratio.

Key Concept Explanation  

For similar polygons, if the perimeter ratio is , then the ratio of any pair of corresponding side lengths is also . This is because perimeter is a linear measurement directly proportional to side lengths.

Step-by-Step Solution  

1. Set up the proportion:  

Let  be the length of the longest side of the larger polygon. Given the perimeter ratio , we can set up the proportion .

2. Solve the proportion:  

Cross - multiply to get

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