Question 825568
bottom, w by y.
{{{2w+2y=42}}};


volume is {{{v=wy*10}}};


From perimeter equation,
w+y=21
w=21-y;
Substitute...
v=(21-y)y*10
{{{v=210y-10y^2}}}



Not finished, short on time here; but quadratic equation in terms of y, so you can find the maximum...
coefficient on y^2 is a negative constant, so v has a maximum.


You can take average of the roots (for when v=0) and that is the y length so you can then use it to find w.  If this a Calculus problem?  You could find derivative and equate to zero to find y...