document.write( "Question 762364: I decide to take up alpaca farming. I will build an alpaca pen next to my house. ( Since it is next to my house, I don't need any fencing on the side where my house is. My house is huge, so I don't have to worry about that side being too short.) I have 800 feet of fencing. What is the most area I can give my alpacas? (The fence can be any shape) \n" ); document.write( "
Algebra.Com's Answer #463906 by Cromlix(4381)\"\" \"About 
You can put this solution on YOUR website!
Use x ft for breadth.
\n" ); document.write( "Length = 800 - 2x
\n" ); document.write( "Area = Breadth * Length
\n" ); document.write( "Area = x(800 - 2x)
\n" ); document.write( "Area(x) = 800x - 2x^2
\n" ); document.write( "Differentiate
\n" ); document.write( "Area'(x)= 800 - 4x
\n" ); document.write( "Area'(x) = 0
\n" ); document.write( " 800 - 4x = 0
\n" ); document.write( " 4x = 800
\n" ); document.write( " x = 200
\n" ); document.write( "Check gradient on either side of 200
\n" ); document.write( "So maximum occurs when x = 200
\n" ); document.write( "So breadth = 200ft
\n" ); document.write( "Length = 400ft
\n" ); document.write( "Maximum area = 800(200) - 2(800)^2
\n" ); document.write( " = 80000ft^2
\n" ); document.write( "Hope this helps.
\n" ); document.write( ":-)
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