Farmer ed has 200 meters of fencing, and wants to enclose a rectangular plot that borders on a river. if farmer ed does not fence the side along the river, find the length and width of the plot that will maximize the area. what is the largest area that can be enclosed

I have no "real" answer, because the river may curve ...

Fun answer: farmer Ed clearly does not realize you can Not create a rectangular plot that borders a river unless it is artificial and instead of dirt, it would Need to be concrete to ensure a constant straight edge; although even in that case, it would no longer Be a river! It would be a mote or channel. So this problem is unsolvable at his current standards.