The point of intersection of the diagonals of a rectangle is 4 cm further away from the smaller side than from the larger side of the rectangle. the perimeter of the rectangle is equal to 56 cm. find the lengths of the sides of the rectangle.

Let the rectangle have length L and width W.
The intersection of the diagonals is at the center of the rectangle. Therefore, its distance to the shorter side would be (L / 2), and the distance to the longer side would be (W / 2). We are given that (L / 2) = (W / 2) + 4. This simplifies to L = W + 8.
The perimeter of the rectangle, 2L + 2W = 56. Substituting L = W + 8:
2W + 16 + 2W = 56
W = 10
L = W + 8 = 18
The rectangle measures 10 cm by 18 cm.