Let d be the distance from the diagonals' intersection and the larger side, so the distance from this point to the smaller side is d + 4 cm. Then d is half of the rectangle's shorter side (call it x), and d + 4 cm is half of the longer side (call it y).
The perimeter of the rectangle is 56 cm, which means
2x + 2y = 56 cm
or
x + y = 28 cm
In terms of d, this becomes
2d + 2 (d + 4 cm) = 28 cm
Solve for d :
2d + 2d + 8 cm = 28 cm
4d = 20 cm
d = 5 cm
Then the sides of the rectangle have length
x = 2d = 10 cm
y = 2 (d + 4 cm) = 2 (13 cm) = 26 cm
