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September 22, 2014

September 22, 2014

Posted by **Mary** on Sunday, January 22, 2012 at 10:57am.

- Math -
**Reiny**, Sunday, January 22, 2012 at 1:14pmMake a sketch

let the length of the whole field be y yds

let each divider line be x yds

so 2y + 4x = 1000

y = 500 - 2x

area = xy

= x(500-2x)

= 500x - 2x^2

I will assume you are taking Calculus, if not you will have to complete the square on the above

d(area)/dx = 500 - 4x = 0 for a max area

4x=500

x = 125

then y = 250

The whole length should be 250 yrd , and each smaller pen should be 125 yrds wide.

max area = 125(250) = 31250 yds^2

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