Question 866147
z = height
y = depth
x = width
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{{{z=2x}}}.
{{{2xy+2xz+2yz=108}}}, total surface area.
{{{2xy+2x*2x+2y*2x=108}}}
{{{4xy+2x^2=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^2}}}
{{{y=(108-2x^2)/(4x)}}}----Actual will use this form
{{{y=27/x-(1/2)x}}}----But could use either of these forms once x is found.
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VOLUME, {{{xyz=x((108-2x^2)/(4x))2x}}}
{{{v=(108-2x^2)x/2}}}
{{{highlight_green(v=(54-x^2)x)}}}


Treating v as a calculus problem, {{{v=54x-x^3}}},
{{{(d/(dx))v=54-3x^2}}}
Where is this equal 0?
{{{54-3x^2=0}}}
{{{54=3x^2}}}
{{{18=x^2}}}
{{{x=sqrt(9*2)}}}
{{{highlight(x=3*sqrt(2))}}}------Using this value of x, calculate for y and z.