Here is the problem:
If 100 feet of fence is used to fence
in a rectangular yard, then the resulting area is given by A = x(50 – x) where x feet is the width of the
rectangle and 50 – x feet is the length. Calculate the length and width that give maximum area. Do not
graph this function.

How would you start? Multipling the 2 equations together?

I am taking this class online, and I am getting lost...

Thanks in advance for the help.

By expanding x(50-x) we get a quadratic.

-x^{2}+50x=0

Use x=\frac{-b}{2a} to find the vertex of this parabola and, consequently, the optimum x value. The y is found my subbing x back into the equation for area.

a=-1 and b=50.

You should notice the max is achieved when the region is a square.

THANKS!