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