Geometry

Question Analysis  

The task is to find the longest side of the larger polygon using the perimeter ratio (6:11) of two similar polygons and the longest side of the smaller polygon (18 units). The key is applying the property that the ratio of corresponding side lengths equals the perimeter ratio.  

Key Concept Explanation  

For similar polygons, if the perimeter ratio is , the ratio of corresponding side lengths is also . Thus, .  

Step-by-Step Solution  

1. Set up the proportion:  

Let  = length of the longest side of the larger polygon.  

The perimeter ratio is , so: