need help! problem solving involving quadratic equations

Ok, here's the question....

A lifeguard uses 700 m of marker buoys to rope off a rectangular swimming area in a lake. One side of the swimming area is a sandy beach.

a) Determine the dimensions that will result in the maximum swimming area.
b) What is the maximum swimming area?

I'm totally stuck.... my head's is spinning right now... please help!

$\displaystyle 2a+b=700$. $\displaystyle A=ab=a\cdot\left(700-2a\right)$ It's roots are: $\displaystyle 0\text{ and } 350$ therefore its maximum is at $\displaystyle a=175$. So the answer: swimming area 175 x 350 which is $\displaystyle 61250\text{ }\rm{m^2}$.

Thanks james_bond.