A javalina rancher wants to enclose a rectangular area and then divide it into f

Question

A javalina rancher wants to enclose a rectangular area and then divide it into five pens with fencing parallel to one side of the rectangle (see the figure below). He has 880 feet of fencing available to complete the job. What is the largest possible total area of the five pens? Note: The answer to this problem requires that you enter the correct units.

Explanation / Answer

Let x be the length of the pens and y be the height of the pens. Then we have 2x + 6y = 880 => x + 3y = 440 => x = 440 - 3y The area is: A = xy = (440 - 3y)y = 440y - 3y^2 => A' = 440 - 6y => 0 = 440 - 6y => 6y = 440 => y = 220/3 So x = 440 - 3(220/3) = 440 - 220 = 220. So the largest possible total area of the five pens is: Area = 220(220/3) = 16,133.3 (repeating) or 48400/3 square feet.

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