Question

The length of a rectangular piece of cardboard is three more than twice the width. A square 2 cm on a side is cut out of each corner. The sides are folded up to form an open box. if the volume of the box is 120cm^3, what were the original dimensions of the cardboard.

Answer 1

L=3+2W

Now, for the box,
L=originalL-4=3+2originalW-4
W=originalW-4

volume=LW*2
120=(3+2originalW-4)(originalW-4)*2
let me now use for originalW, w'

60=(2w'-1)(w'-4)
60=2w'^2-8w'-w'+4
56=2w'^2-9w'
2w'^2-9w'-56=0
(2w+7)(w'-8)=0
w'=8
l'=2(8)+3=19

check...volume of box then is
V=2*(8-4)(19-4)=4*15*2=120