Question 946067
Let x and y be the bottom dimensions.

Volume is {{{20xy=990}}}.

Total area is {{{2*20x+2*20y+2*xy=675}}}.


Simplify the system.
{{{system(2xy=99,40x+40y+2xy=675)}}}


A bit of some algebra steps, but solve the first equation for either variable and substitute into the second equation.--------------BUT recognize that both equations have a term, 2xy.  Make use of that!!


{{{40x+40y+(99)=675}}}, substituting for 2xy.
{{{40x+40y-675+99=0}}}
{{{40x+40y-576=0}}}
NOW use the first equation again but solved for either variable in terms of the other variable:  {{{y=99/(2x)}}}.
Substitute for that variable.
{{{40x+40(99/(2x))-576=0}}}
{{{40x+20*99/x-576=0}}}
{{{40x^2+198-576x=0}}}----Do you know what was done for this step?
{{{20x^2-288x+99=0}}}


Not sure if that is factorable.  Find discriminant.
{{{288^2-4*20*99}}}
{{{82944-8*99*10}}}
{{{82944-7920}}}
{{{67104}}}
{{{9*7456=9*4*1864=9*4*4*466=9*4*4*2*233}}}, the big factor being prime.
Discriminant is {{{highlight_green((3*4)^2*(2*233))}}}.


{{{x=(288+- sqrt(3^2*4^2*466))/(400)}}}

{{{x=(288+- 12*sqrt(466))/400}}}

{{{highlight(x=(72+-  3*sqrt(466))/100)}}}
Not really finished but more than half the way to it.