document.write( "Question 909053: Beth has 2200 feet of fencing available to enclose a rectangular field. One side of the field lies along a river, so only three sides require fencing.
\n" ); document.write( "(a) Express the area A of the rectangle as a function of x, where x is the length of the side parallel to the river. For what value of x is the area largest? \n" ); document.write( "

Algebra.Com's Answer #551560 by lwsshak3(11628) $\"\"$ $\"About$

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Beth has 2200 feet of fencing available to enclose a rectangular field. One side of the field lies along a river, so only three sides require fencing.
\n" ); document.write( "(a) Express the area A of the rectangle as a function of x, where x is the length of the side parallel to the river. For what value of x is the area largest?
\n" ); document.write( "***
\n" ); document.write( "x=length of side parallel to river
\n" ); document.write( "(2200-x)/2=width of rectangular area
\n" ); document.write( "Area=length*width
\n" ); document.write( "A(x)=x(2200-x)/2
\n" ); document.write( "A(x)=(2200x-x^2)/2
\n" ); document.write( "A(x)=-1/2(x^2-2200x)
\n" ); document.write( "complete the square:
\n" ); document.write( "A(x)=-1/2(x^2-2200x+(1100^2))+1100^2/2
\n" ); document.write( "A(x)=-1/2(x-1100)^2+605000
\n" ); document.write( "This is an equation of a parabola that opens down with vertex at (1100,605000)
\n" ); document.write( "For what value of x is the area largest? x=1100 ft \n" ); document.write( "

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