Geometry

Question Analysis  

The task is to determine the ratio of the perimeters of two similar polygons using their given side-length ratio (2:7). The key is applying the property that the perimeter ratio of similar polygons equals their side-length ratio.  

 

Key Concept Explanation  

For similar polygons, the ratio of corresponding side lengths is equal to 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 and match side-length ratios, while area ratios are squared.  

Reversing the ratio order due to misreading the problem.  

 

Summary  

The ratio of the perimeters is 2 : 7, identical to the given side-length ratio.  

Problem-Solving Tips:  

Remember: Perimeter ratio = side-length r...