Let's say you have two similar polygons and the ratio of their perimeters is 6: 1. what is the ratio of corresponding sides?

Well if we had a four sided polygon with the sides of x1, x2, x3, x4. Where the perimeter is: (x1 + x2 + x3 + x4), A similar polygon will have proportional sides. Their sides would be >  kx1, kx2, kx3, kx4sooo... The perimeter is: (kx1 + kx2 + kx3 + kx4) > k(x1 + x2 + x3 + x4) therefore the ratio is the same because the perimeter and sides are the same. So 6:1

Hope this helps!