Let's say you have two similar polygons and the ratio of their perimeters is 4: 1. what is the ratio of corresponding sides?

Assuming two regular polygons A and B with same side n and length of sides a and b, their perimeters are:

A = a n

B = b n

Given that A / B = 4, therefore:

A / B = a n / b n

4 = a / b

So the ratio of their sides is also 4:1

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.