Let's pick a square with side lengths of 100 perimeter = 400
area = 100x 100 = 10, 000
then the rectangle will have side lengths of 88.88888 and 111.11111 Perimeter = 400
area = 88.88888... x 111.11111...= 9876.54321
ratio of rectangle to square areas = 9876.45321/10000 = ~ 80/81