document.write( "Question 933281: I need help with solving this problem. Here is the question: Chris has purchased 50 feet of fencing to build a rectangular pen along the side of a hay barn. Therefore, the barn can serve as one side of the pen.\r
\n" ); document.write( "\n" ); document.write( "a) Determine an algebraic function for the area of the pen.
\n" ); document.write( "b) Find the dimensions of the pen that will yield the maximum area. \n" ); document.write( "
Algebra.Com's Answer #566733 by lwsshak3(11628)\"\" \"About 
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Chris has purchased 50 feet of fencing to build a rectangular pen along the side of a hay barn. Therefore, the barn can serve as one side of the pen.
\n" ); document.write( "a) Determine an algebraic function for the area of the pen.
\n" ); document.write( "b) Find the dimensions of the pen that will yield the maximum area.
\n" ); document.write( "***
\n" ); document.write( "let x=width
\n" ); document.write( "let y=length (side facing barn)
\n" ); document.write( "2x+y=50
\n" ); document.write( "y=50-2x
\n" ); document.write( "Area,A=xy=x(50-2x)
\n" ); document.write( "A=50x-2x^2
\n" ); document.write( "A=-2x^2+50x
\n" ); document.write( "complete the square:
\n" ); document.write( "A=-2(x^2-25x+(12.5)^2)+312.5
\n" ); document.write( "A=-2(x-12.5)+312.5 (algebraic function for the area of the pen)
\n" ); document.write( "This is an equation of a parabola that opens down with vertex at (12.5,312.5)
\n" ); document.write( "dimensions of pen to yield maximum area of 312 sq ft:
\n" ); document.write( "width=12.5 ft
\n" ); document.write( "length=50-2x=50-25=25 ft
\n" ); document.write( " \n" ); document.write( "
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