One polygon has a side of length 2 feet. a similar polygon has a corresponding side of length 4 feet. the ratio of the perimeter of the smaller polygon to the larger is

This is the concept of proportionality;we are required to find the ratio of perimeter of smaller polygon to larger polygon.
To solve the question we need to know that since the length of the corresponding sides of each polygon is equal, the ratio of their perimeters is the the same as the ratio of the sides;
thus
[perimeter of small polygon]/[perimeter of larger polygon]=[side length of small polygon]/[side length of larger polygon]
thus  the ratio will be:
2/4=1/2
the answer is 1/2