Simeon has a rope that is \(108\) cm long and is asked to cut the rope once so that one of the pieces can be arranged, with its two ends touching, to form a square, and the other piece can be arranged, with its two ends touching, to form a rectangle with one side length of \(6\) cm. Furthermore, the area of the square will be equal to the area of the rectangle.
Where should Simeon make the cut to the original piece of rope?