The rectangle is 10 cm by 18 cm.
Let x represent the distance from the center of the rectangle to the longer side. Then the distance to the shorter side is x+4. The short side of the rectangle will have length 2x, and the long side will have length 2(x+4) = 2x+8.
The perimeter is twice the sum of the side lengths, so is ...
56 = 2(2x +(2x+8)) = 8x +16
40 = 8x . . . . . . . subtract 16
40/8 = x = 5 . . . divide by the coefficient of x
The side lengths are 2x=10 and 2x+8 = 18 centimeters.