Question 988965
length L
width w
A for AREA

perimeter is 60 feet, equal to the amount of fencing.
{{{2w+2L=60}}}
{{{w+L=30}}}


{{{A=wL}}}
{{{A=w(30-w)}}}
{{{A=30w-w^2}}}
{{{A=-w^2+30w}}}------Just as you have.


Your question is, what is w and L for maximum area A ?


w and L must be each greater than 0. 
A is a parabola function and {{{A=-w^2+30w}}}  has a maximum point for its vertex; and A has two x-axis intercepts.  The maximum value for A occurs in the exact middle of the roots.  w is really the HORIZONTAL number line and A is for the vertical number line.  


Roots for A?
{{{-w^2+30w=0}}}
Solve for w, and find what is the value in the middle?
Now, what is A at that middle value of w?