document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106355>Question 106355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer plans to fence a rectangular grazing area along a river with 300 yards of fence. Write an expression for the area A of grazing land in terms of the width w of the rectangle. Also, what is the largest area he can enclose? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77568 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77568\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A farmer plans to fence a rectangular grazing area along a river with 300 yards of fence. Write an expression for the area A of grazing land in terms of the width w of the rectangle. Also, what is the largest area he can enclose?<BR>\n" );
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document.write( "Since one side is the river, the rectangle's fence perimeter will be:<BR>\n" );
document.write( "L + 2W = 300<BR>\n" );
document.write( "L = 300 - 2W<BR>\n" );
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document.write( "Area = Length * Width<BR>\n" );
document.write( "Substitute (300-2W) for L:<BR>\n" );
document.write( "A = W(300 - 2W)<BR>\n" );
document.write( "A = -2W^2 + 300W; this would be the expression<BR>\n" );
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document.write( "This is a quadratic equation, Find the axis of symmetry, x = -b/(2a)<BR>\n" );
document.write( "In our equation it would be:<BR>\n" );
document.write( "W = -300/(2*-2)<BR>\n" );
document.write( "W = -300/-4<BR>\n" );
document.write( "W = +75 is the width for max area:<BR>\n" );
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document.write( "Find the max area, substitute 75 for W<BR>\n" );
document.write( "A = -2(75^2) + 300(75)<BR>\n" );
document.write( "A = -2(5625) + 22500<BR>\n" );
document.write( "A =  -11250  + 22500<BR>\n" );
document.write( "A = 11250 sq ft is the max area<BR>\n" );
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document.write( "If you plot this, y = area and x = width<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-50%2C+200%2C+-1000%2C+12000%2C+-2x%5E2+%2B+300x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-50%2C+200%2C+-1000%2C+12000%2C+-2x%5E2+%2B+300x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " </SPAN>\n" );
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