If a farmer has 100 meters of fence what is the maximum area if he has a barn?

The maximum area is 625 m². The maximum area can be found using a system of equations with two unknowns. By expressing the Area equation with only a single variable, the area is maximized wherever the first derivative of the equation is equal to zero. We find that the area is maximized when the two opposite sides of the barn are set to 25 m. Therefore, every side mesures 25 m and the maximum area is 625 m².