Question

A rectangular 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?

Answer 1

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.

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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.