Question 849981

x and y, the dimensions.  Uncut cardboard.
{{{xy=945}}}.


Cutting off corners 3 by 3 square inches.
Base is {{{(x-2*3)(y-2*3)}}}
Height is simply 3.

VOLUME is {{{3(x-6)(y-6)=1755}}}.
This volume equation can be a little bit more simplified initially:
Volume is {{{(x-6)(y-6)=585}}}.


Let me leave this unfinished.  The two equations to use are the system:
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xy=945
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(x-6)(y-6)=585
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The second equation, the volume one gives 
{{{xy-6x-6y+36=585}}}
And substituting for {{{xy=945}}} you get after a simplification,
{{{-6x-6y+396=0}}}
{{{x+y-66=0}}}
Again substituting from the area as {{{y=945/x}}}, obtain
after further steps,
.
{{{highlight_green(x^2-66x+945=0)}}}
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Using the general solution to a quadratic equation gives
{{{x=(66+sqrt(576))/2}}}
{{{highlight(x=45)}}}  (we use the positive square root).
From this and the area equation again, {{{highlight(y=21)}}}.