SOLUTION: suppose you want to build a rectangular bozo such that its height is double its width.(the depth of the box could be anything.) if you want the surface area to be 108 square feet,

Algebra ->  Surface-area -> SOLUTION: suppose you want to build a rectangular bozo such that its height is double its width.(the depth of the box could be anything.) if you want the surface area to be 108 square feet,       Log On


   

Question 866147: suppose you want to build a rectangular bozo such that its height is double its width.(the depth of the box could be anything.) if you want the surface area to be 108 square feet, and you want the volume to be as large as possible, what should the dimensions of the box be?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
z = height
y = depth
x = width
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z=2x.
2xy%2B2xz%2B2yz=108, total surface area.
2xy%2B2x%2A2x%2B2y%2A2x=108
4xy%2B2x%5E2=108
Sensing advantage in having volume formula all in one variable, x, the transformed surface area formula should be solved for y.
4xy=108-2x%5E2
y=%28108-2x%5E2%29%2F%284x%29----Actual will use this form
y=27%2Fx-%281%2F2%29x----But could use either of these forms once x is found.
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VOLUME, xyz=x%28%28108-2x%5E2%29%2F%284x%29%292x
v=%28108-2x%5E2%29x%2F2
highlight_green%28v=%2854-x%5E2%29x%29

Treating v as a calculus problem, v=54x-x%5E3,
%28d%2F%28dx%29%29v=54-3x%5E2
Where is this equal 0?
54-3x%5E2=0
54=3x%5E2
18=x%5E2
x=sqrt%289%2A2%29
highlight%28x=3%2Asqrt%282%29%29------Using this value of x, calculate for y and z.