The length of a rectangular piece of cardboard is 2 cm greater than its width. If the length and the width were each decreased b
y 1 cm, the area of the cardboard would be decreased by 27 cm². What are the dimensions of the original piece of cardboard? Write and solve an equation to represent the problem.
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.
