If the perimeters of a rectangle and a square are equal and the ratio of two adjacent sides of the rectangle is 1 : 2 then the ratio of area of the rectangle and that of the square is
let l, b are the length & breadth of a rectangle, and s be the side of a square.Â
l:b = 2:1 so l = 2b.
given that perimeters of both are same,Â
2(l+b) = 4sÂ
2(2b+b) = 4s
6b = 4s
b/s = 2/3
area of rectangle = l*b = 2b*b = 2$$b^{2}$$
area of square = $$s^{2}$$
ratio = (2$$b^{2}$$)/($$s^{2}$$)
    = 2$$(b/s)^{2}$$
    = 2(4/9) = 8/9 = 8 : 9
so the answer is option D.
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