document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=186379>Question 186379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a farmer has 500 feet of fencing with which to build a rectangular livestock pen and wants to enclose the maximum area.<BR>\n" );
document.write( "use a variable to label length and width of the rectangle <BR>\n" );
document.write( "find a variable expression for the area of the pen \r<BR>\n" );
document.write( "\n" );
document.write( "this is totally killing me can someone please help??? thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139738 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=139738\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a farmer has 500 feet of fencing with which to build a rectangular livestock<BR>\n" );
document.write( " pen and wants to enclose the maximum area.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "use a variable to label length and width of the rectangle<BR>\n" );
document.write( "find a variable expression for the area of the pen<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = width of the pen<BR>\n" );
document.write( "Let L = length of the pen<BR>\n" );
document.write( ":<BR>\n" );
document.write( "write an equation for the total fencing available (the perimeter)<BR>\n" );
document.write( "2L + 2x = 500<BR>\n" );
document.write( "Simplify, divide equation by 2<BR>\n" );
document.write( "L + x = 250<BR>\n" );
document.write( "L = (250-x)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The area = L * x, substitute (250-x) for x<BR>\n" );
document.write( "A = x(250-x)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "A = -x^2 + 250x; this is the variable expression for the area of the pen<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can calculate the max area using the axis of symmetry formula x=-b/(2a)<BR>\n" );
document.write( "In this problem: <BR>\n" );
document.write( "x = -250/(2*-1)<BR>\n" );
document.write( "x = -250/-2<BR>\n" );
document.write( "x = 125 is the width for max area<BR>\n" );
document.write( "Note that would be a square: L = 250-x, right?<BR>\n" );
document.write( "L = 250 - 125<BR>\n" );
document.write( "L = 125 also<BR>\n" );
document.write( ":<BR>\n" );
document.write( "To find the actual area: substitute 125 for x in the equation<BR>\n" );
document.write( "A = -(125^2) + 250(125)<BR>\n" );
document.write( "A = -15625 + 31250<BR>\n" );
document.write( "A = + 15625 sq/ft is the max area<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Note this corresponds to a square field: 125 * 125 = 15625 sq/ft<BR>\n" );
document.write( ":<BR>\n" );
document.write( "To graph this equation, area = y; write it: <BR>\n" );
document.write( "y = -x^2 = 250x<BR>\n" );
document.write( "On a TI83 or similar just enter y= -x^2 +25x, scale it x:-100,+300; y:-2000,+16000<BR>\n" );
document.write( ";<BR>\n" );
document.write( "it should look like this<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-100%2C+300%2C+-5000%2C+16000%2C+-x%5E2%2B250x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-100%2C+300%2C+-5000%2C+16000%2C+-x%5E2%2B250x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Note the max area (y) occurs when x = 125<BR>\n" );
document.write( ":<BR>\n" );
document.write( "If you have to plot this on graph paper, you have to make up an x/y table<BR>\n" );
document.write( "and plot about a dozen points from x=0 to x=+250. let me know if you have<BR>\n" );
document.write( " to do that and don't know how to do it. Carl<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );