Carol has 2,000 ft of fencing to fence in a rectangular horse corral. x 1000 -

Algebra
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Carol has 2,000 ft of fencing to fence in a rectangular horse corral.
x1000 - x
(a) Find a function that models the area A of the corral in terms of the width x of the corral. 
A(x) =

(b) Find the dimensions of the rectangle that maximize the area of the corral. 
width     ft
length     ft
Jul 8th, 2015

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.

Please ask if anything is unclear.
Jul 8th, 2015

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