let 'w' represent the width of the rectangle, then 'w/2' represents the length of the side of the square

the perimeter of the rectangle is 16 units greater than the perimeter of the square:

perimeter of the square: 2(w/2 + w/2) = 2w

perimeter of the rectangle is then '2w+16'

the area of the rectangle is 8 times the are of the square:

area of the square: (w/2)*(w/2) = w^2/4

area of the rectangle: 8(w^2/4) = 2w^2

let 'l' represent the length of the rectangle, then for perimeter and area of the rectangle we have

2w+16 = 2(l+w)

2w^2 = l*w, or l = (2w^2)/w = 2w

substituting 'l' with '2w':

2w+16 = 2(2w+w)

solving for 'w' we have w=4

2*4 = 8

the rectangle has dimensions 4x8

4/2 = 2

the square has dimensions 2x2