A farmer has 100 m of fencing for a rectangular plot beside a straight wall, so only three sides need fencing. What is the largest area, in m², he can enclose?

Explanation

1. 01

   With the side parallel to the wall $y$ and the other two $x$: $2x + y = 100$, area $A = x(100 - 2x)$.

2. 02

   $A' = 100 - 4x = 0$ at $x = 25$, so $y = 50$ and $A = 1250$.