SOLUTION: 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

Click here to see ALL problems on Rectangles

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.
B.) find the dimensions of the box.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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