How do you find the ratio of the perimeter of two similar rectangles?

The ratio of the perimeters is equal to the scale factor. If rectangle #1 has sides L and W, then the perimeter is 2*L1 + 2*W1 = 2*(L1 + W1).

If rectangle # 2 is similar to #1 and sides are scaled by a factor S, so that L2 = S*L1 and W2 = S*W1, the perimeter of rectangle #2 is 2*(L2 + W2)= 2*(S*L1 + S*W1) = S*2*(L1 + W1) = S*(perimeter of rectangle #1).