Geometry

Question Analysis  

The task is to determine the ratio of the side lengths of two similar polygons given their perimeters (54 units for the first, 90 units for the second). The key is using the property that the ratio of side lengths of similar polygons equals the ratio of their perimeters.  

 

Key Concept Explanation  

For similar polygons, the ratio of corresponding side lengths is equal to the ratio of their perimeters. If the perimeters are and , then .  

 

Step-by-Step Solution  

1. Set up the perimeter ratio:  

Ratio of the first polygon’s perimeter to the second:  

2. Simplify the ratio:  

Divide both terms by their greatest common divisor (18):