Geometry

Question Analysis  

The task is to determine the ratio of the perimeters of two similar polygons given their side-length ratio (3:1). The key is recognizing that perimeter ratios of similar polygons equal their side-length ratios.  

 

Key Concept Explanation  

For similar polygons, the ratio of corresponding side lengths equals the ratio of their perimeters. If the side-length ratio is , the perimeter ratio is also .  

 

Step-by-Step Solution  

1. Apply the similarity property:  

Given the side-length ratio , the perimeter ratio is directly .  

 

Common Mistakes  

Confusing perimeter ratios with area ratios: Perimeter ratios are linear, while area ratios are squared.  

Misreading the order of the ratio (e.g., swapping "larger" and "smaller" polygon).  

 

Summary  

The ratio of the perimeters is 3 : 1, identical to the given side-length ratio.  

Problem-Solvin...