Question 632571: I have a piece of cardboard, twice as long as it is wide. I will cut 4x4 squares out of each corner, so i fold up the corners and use it as a tray. The volume of the tray will be 96 cubic inches. How large is the piece of cardboard?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! I have a piece of cardboard, twice as long as it is wide.
I will cut 4x4 squares out of each corner, so i fold up the corners and
use it as a tray.
The volume of the tray will be 96 cubic inches.
How large is the piece of cardboard?
:
let x = the width of the cardboard
then
2x = the length of the cardboard
:
The dimensions of the tray
the 4" squares will reduce both dimensions of the cardboard by 8"
:
(x-8) = the width of the tray
(2x-8) = the length of the tray
4 inches = the height of the tray
:
The volume of the tray, Length * Width * height = 96 cu/in
(2x-8)*(x-8)*4 = 96
FOIL
4(2x^2 - 16x - 8x + 64) = 96
4(2x^2 - 24x + 64) = 96
8x^2 - 96x + 256 = 96
A quadratic equation
8x^2 - 96x + 256 - 96 = 0
8x^2 - 96x + 160 = 0
simplify, divide by 8
x^2 - 12x + 20 = 0
Factors to
(x-2)(x-10) = 0
Two solutions but only one will make sense
x = 10 inches is the width
then
20 inches is the length
:
The original cardboard is 20 by 10
:
:
Check this by finding the volume
(20-8)*(10-8)*4 = 96
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