A rectangular piece of cardboard, whose area is 216 square centimeters, is made into an open box by cutting a 2-centimeter square from each corner and turning up the sides. if the box is to have a volume of 224 cubic centimeters, what should the original dimensions of the cardboard start with

let the length of the original cardboard be x and width be y.
Area=xy=216
thus y=216/x
after cutting 2 cm from the edges, the dimensions will be:
(x-4) cm by (216/x-4) by 2 cm
thus the volume will be:
V=L×W×H
V=(216/x-4)×(x-4)×2=224
thus solving for x we get:
x=12 or x=18
Hence:
length=18cm width=12 cm