Geometry

Question Analysis  

The core task is to find the ratio of the side lengths of two similar polygons, M and N, using their given perimeters (30 units for M and 78 units for N). The key lies in applying the property that the ratio of side lengths of similar polygons is equal to the ratio of their perimeters.

Key Concept Explanation  

For similar polygons, if the perimeters of two polygons are  and , the ratio of their corresponding side lengths  and  follows the relationship . This is because perimeter, being a linear measurement, scales proportionally with the side lengths.

Step-by-Step Solution  

1. Set up the perimeter ratio:  

Write the ratio of the perimeter of polygon M to polygon N:

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