Geometry

Question Analysis  

The task is to determine the ratio of the perimeters of two similar polygons given their side-length ratio (4:9). The key is applying the property that perimeter ratios of similar polygons equal their side-length ratios.  

Key Concept Explanation  

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

Step-by-Step Solution  

1. Apply the similarity property:  

Given the side-length ratio , the perimeter ratio is directly . No calculations are needed—this is a direct application of the similarity principle.  

Common Mistakes  

Confusing perimeter with area ratios: Forgetting that perimeter ratios are linear () while area ratios are squared (

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