Question 1003749
A box with no top is to be formed from a rectangular cardboard by cutting 4 cm squares from the corners and folding up the sides.
 The length of the box is to be 2 cm more than its width and its volume is to be 252 cubic cm.
:
A.) find the dimensions of the sheet of cardboard.
let L = the length of the cardboard
let w = the width of the card board
Cutting 4" corners from the sheet means the height is 4" and the dimensions are:
(L-8) = the length of box
(W-8) = width of the box
:
The volume of the box equation
(L-8)*(w-8)*4 = 252
divide both sides by 4
(L-8)*(w-8) = 63
:
"The length of the box is to be 2 cm more than its width"
L - 8 = w - 8 + 2
L = w - 8 + 2 + 8
L = w + 2
:
(L-8)*(w-8) = 63
Replace L with (w+2)
((w+2)-8)*(w-8) = 63
(w-6)(w-8) = 63
FOIL
w^2 - 8w - 6w + 48 = 63
w^2 - 14w + 48 - 63 = 0
w^2 - 14w - 15 = 0
Factors to
(w-15)(s+1) = 0
The positive solution is all we want here
w = 15 cm is the width of the sheet of cardboard
then
15 + 2 = 17 cm is the length
:
The dimensions of the sheet of cardboard: 17 by 15 cm

B.) find the dimensions of the box.
subtract 8 cm from length and width
9 by 7 by 4 cm is dimensions of the box
;
:
Check this by finding the volume using these value
9 * 7 * 4 = 252 cu/cm