SOLUTION: Peter has a piece of metal 18 inches wide and 20 inches long, he wants to make an open box with a volume of 200 inches cubed, by cutting out a square of the same size from each cor

Question 712929: Peter has a piece of metal 18 inches wide and 20 inches long, he wants to make an open box with a volume of 200 inches cubed, by cutting out a square of the same size from each corner and folding up the edges of the piece of metal. To the nearest tenth of an inch what is the length(s) of a side of the square cut from each corner? Round to the nearest hundredths
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Peter has a piece of metal 18 inches wide and 20 inches long, he wants to make an open box with a volume of 200 inches cubed, by cutting out a square of the same size from each corner and folding up the edges of the piece of metal.
To the nearest tenth of an inch what is the length(s) of a side of the square cut from each corner
:"
Let x = length of the side of the square to be removed from each corner
then
(20-2x) = the length of the box
(18-2x) = the width of the box
x = the height of the box
:
h * L * W = V
therefore
x(20-2x)(18-2x) = 200
FOIL
x(360 - 40x - 36x + 4x^2) = 200
x(360 - 76x + 4x^2) = 200
360x - 76x^2 + 4x^2 - 200 = 0
4x^3 - 76x^2 + 360x - 200 = 0
simplify, divide by 4
x^3 - 19x^2 + 90x - 50 = 0
find the 0 by graphing

x intercept occurs when x = .64 inches, the side of of the removed square
:
:
You can confirm this yourself by finding the volume
(20-1.28)*(18-1.28) * .64 =
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