Question 1061434
x and x bottom dimensions;
y, the height dimension;


{{{x^2+x^2+4xy=52}}}
{{{2x^2+4xy=52}}}


VOLUME for the box, v is
{{{v=yx^2}}}



Solve the area equation for y in terms of x.
{{{4xy=52-2x^2}}}
{{{2xy=26-x^2}}}
{{{y=(26-x^2)/(2x)}}}


Substitute this for y in the volume equation.
{{{v=((26-x^2)/(2x))x^2}}}

{{{v=((26-x^2)x^2)/(2x)}}}

{{{v=((26-x^2)x)/2}}}

{{{highlight(v=13x-(1/2)x^3)}}}