Question 237341: A Box with an open top is formed by cutting squares out of the corners of a rectangular piece of cardboard and then folding up the sides. If x represents the length of the side of the square cut from each corner, and if the original piece of cardboard is 13 inches by 11 inches, what size square must be cut if the volume of the box is to be 99 cubic inches?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A Box with an open top is formed by cutting squares out of the corners of a rectangular piece of cardboard and then folding up the sides.
If x represents the length of the side of the square cut from each corner, and if the original piece of cardboard is 13 inches by 11 inches, what size square must be cut if the volume of the box is to be 99 cubic inches?
:
The dimension of the box will be: L * W* H
(13-2x)*(11-2x)*x
;
The volume:
x(13-2x)*(11-2x) = 99
FOIL
x(143 - 48x + 4x^2) = 99
:
4x^3 - 48x^2 + 143x - 99 = 0
:
Hopefully it's an integer, we know it's a low value
:
Try x=1 using synthetic division
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1 |4 - 48 + 143 - 99
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I got this to come out with no remainder
:
Check x = 1, the side of the cut out squares
(13-2)(11-2) * 1 =
11 * 9 * 1 = 99 cu/in
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