9514 1404 393
Answer:
 13 cm wide;  15 cm long
Step-by-step explanation:
Let w represent the original width. Then the original length is (w+2) and the original area is w(w+2). After the decrease, the width is (w-1) and the length is (w+1). The decreased area is (w-1)(w+1). The difference between these areas is 27, so we have ...
 w(w+2) -(w-1)(w+1) = 27
 w^2 +2w -(w^2 -1) = 27
 2w +1 = 27
 w = (27-1)/2 = 13
The original piece of cardboard was 13 cm wide and 15 cm long.
