Question

A farmer with 700 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?

Answer 1

Answer:

  12250 ft²

Step-by-step explanation:

Let x represent the length of a partition. Then the total length of that and all of the fence segments parallel to it will be 5x. The length of the side of the rectangular area in the perpendicular direction will be ...

  (700 -5x)/2

Then the total area of the 4 pens is ...

  Area = (x)(700 -5x)/2 = (5/2)(x)(140 -x)

This function describes a parabola opening downward, with zeros at x=0 and x=140. Its vertex (maximum) will be halfway between those zeros, at x=70.

Then the maximum area is ...

  Area = (5/2)(70)(140 -70) = (5/2)(4900) = 12,250 . . . . ft²