If L=length and W=width, perimeter=2(L+W)=48 so L+W=24 and LW=72.
W=24-L so L(24-L)=72 and 24L-L²=72. So L²-24L=-72. Complete the square:
L²-24L+144=-72+144=72,
(L-12)²=72=2×36,
L-12=±√(2×36)=±6√2=8.485cm approx.
Therefore L, W=12+6√2, 12-6√2=20.485cm, 3.515cm.
The dimensions of the rectangle are 20.485cm×3.515cm (approx).