Question

You have P = 472 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the dimensions (width x and length y) of the plot that will maximize the area.

Answer 1

The width would be 236 and the lengths would be 118

Use the equations 2L+W=472 and W*L=MAX
Change the first equation to W=472-2L and plug this into the other equation
(472-2L)(L)=MAX
472L-2L^2=M (take derivative)
472-4L=0 (set to 0 to find the max value)
4L=472 
L=118 
Plug into original to get W=236

Hope this helps!