Geometry

Question Analysis  

The task is to find the ratio of the side lengths of two similar polygons (A and B) given their perimeters (24 units and 36 units). The key is using the property that the ratio of perimeters of similar polygons equals the ratio of their corresponding side lengths.  

 

Key Concept Explanation  

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

 

Step-by-Step Solution  

1. Set up the perimeter ratio:  

The ratio of the perimeters of polygon A to polygon B is:  

 

2. Simplify the ratio:  

Divide both the numerator and denominator by their greatest common divisor (12):  

Thus, the ratio of the side lengths of A to B is