A farmer has 1200 feet of fence to enclose a rectangular fie

A farmer has 1200 feet of fence to enclose a rectangular field bordering a river. Only 3 sides of the rectangle need fence and no fence is needed along the river. Find the maximum area of the rectangle.

Solution

Let the lenght of rectangle be l

and width be w

Length of fence = 2w +l = 1200

Area = l*w = (1200 -2w)w = -2w^2 +1200w

Maximum area is attained at vertex of quadratic equation above:

w = -b/2a = -1200/(2*-2) = 300 feet

l= 1200 -2w = 1200 -2*300 = 600 feet

maximum Area = l*w = 300*600 = 180000 ft^2