Quadratic Functions

Question

A farmer with 1200m 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

Let x = length of each subdivision and y = length of each of the other sides

2y + 5x = 1200 So, y = (1200 - 5x) / 2

Area = A = xy = (1/2)(x)(1200 - 5x) = (1/2)(-5x² + 1200x)

A' = (1/2)(-10x + 1200) = 0 when x = 120

Maximum area when x = 120

Maximum area = (1/2)(120)(600) = 36000 m²

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Answer 2

1200/4=300

So 301*299=89.999sq/ft