SOLUTION: 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

Algebra ->  Volume -> SOLUTION: 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      Log On


   

Question 798811: 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 20 inches by 15 inches, what size must be cut if the volume of the box is to be 336 cubic inches?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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 20 inches by 15 inches, what size must be cut if the volume of the box is to be 336 cubic inches?
:
The dimensions of the box can be represented by:
(20-2x) by (15-x) by x, which is he height
therefore the volume
(20-2x)*(15-2x)*x = 336
FOIL
x(300 - 40x - 30x + 4x^2) = 336
Which is
4x^3 - 70x^2 + 300x - 336 = 0
Graphically
+graph%28+300%2C+200%2C+-2%2C+5%2C+-500%2C+100%2C+4x%5E3-70x%5E2%2B300x-336%29+
Two solutions, let's use the integer solution x=4 is the side of the square
:
Check (20-8)*(15-8)*4 = 336