Description
Carol has 2,000 ft of fencing to fence in a rectangular horse corral.
x | 1000 - x |
(a) Find a function that models the area A of the corral in terms of the width x of the corral.
(b) Find the dimensions of the rectangle that maximize the area of the corral.
A(x) = |
(b) Find the dimensions of the rectangle that maximize the area of the corral.
width | ft |
length | ft |
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Explanation & Answer
Hello!
If one side (width) of a rectangle is x ft, then the opposite is also x and adjacent sides (length) have length of (2000 - 2x)/2 = 1000-x (as at your picture).
So a) the area A(x) = x*(1000-x) (square fts).
b) A(x) = -x^2 + 1000x = -(x-500)^2 +500^2 <= 500^2.
Therefore A(x) has a maximum at x=500(ft). Width=500ft and length=1000-500=500ft.
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