If the ratio is always 2:3 surely then to work out the length of the sides, divide the area by 6 to give you a number 'a'.
One side will be 2 x the square root of 'a' the other will be 3 x the square root of 'a'.
In your example above a = 1 so square root of a also = 1, but it should work for any size rectangle that is of the ratio 2:3…I think…seems logical to me.
e.g. area = 24, then 24/6 = 4, so one side is 2 x 2 = 4 and the other is 3 x 2 = 6.