Let the length of the original rectangle be xcm, and the length: width =3:2, and the width of the original rectangle can be 2/3xcm.

According to the meaning of the question (the areas of the strips cut twice are equal), it is 4×2/3x=5(x-4).

8/3x=5x-20

-7/3x=-20

x=60/7

So 2/3x=2/3×60/7=40/7

The length of the original rectangle is 60/7cm and the width of the original rectangle is 40/7cm.