Arectangular corral is enclosed using 120 m of fencing. the corral uses the side of a barn as one of its sides, so fencing is required on three sides of the rectangular region. what dimensions would maximize the area enclosed by the fence?

Area is maximized when half the fence is used parallel to the barn and the other half is perpendicular. Dimensions of 30 m by 60 m will maximize the enclosed area.


Let x represent the fence length parallel to the barn. The area is
.. A = x(120-x)/2
This is the equation of a downward-opening parabola with vertex (maximum) at x=60, halfway between the zeros at x=0 and x=120.