Question 1010811
Most of the way through, but short of complete finish:


y, height
x, length
z, width


The description gives from these chosen variables,
{{{system(y=5z,xyz=1800)}}}
and the area function you want, depending on name you choose, 
{{{A=2xy+2yz+2xz}}}.


Substitutions to put A as a function of just one single variable...
{{{x(5z)z=1800}}}
{{{5xz^2=1800}}}
but z is width, and the question asks for LENGTH to minimize area.
Try again...
-
{{{z=y/5}}}
Use in the volume,
{{{xy(y/5)=1800}}}
still giving a square for what we want to substitute.
-

Try first aiming for one of the other variables for the single variable in A.
Go back to description, and substitute for y in A.
{{{A=2x(5z)+2*5zz+2xz}}}
{{{A=10xz+10z^2+2xz}}}
{{{A=12xz+z^2}}}-------want to eliminate, subst for x or z...


Look again at description.
{{{x(5z)z=1800}}}
{{{5xz^2=1800}}}
{{{x=1800/(5z^2)=360/z^2}}}------Substitute for x in A.


{{{A=12(360/z^2)z+z^2}}}
{{{highlight(A=4320/z+z^2)}}}-------Variable z must be used, take derivative, and find what makes A the minimum, and then find the corresponding x value, the asked for  length.


---------
continuing,


{{{A=4320/z+z^2}}}


{{{dA/dz=2z-4320/z^2}}}  You fill in the steps to that.


Set deriv to 0.
{{{2z(z^2)/z^2-4320/z^2=0}}}
{{{(2z^3-4320)/z^2=0}}}
The denominator does not take meaning here ...
{{{2z^3-4320=0}}}
{{{z^3-2160=0}}}
{{{z^3=2160}}}
and you can fill-in the steps...
{{{highlight(z=6sqrt(10))}}}


Again use the equations from the description to reach the corresponding value for x, the length.