document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171903>Question 171903</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/013600492x/algebrahomeworkh>Algebra & Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> This problem is in the review section about the farmer and fencing.\r<BR>\n" );
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document.write( "A farmer with 10,000 meters of fencing wants to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sided.  What is the largest area that can be enclosed?\r<BR>\n" );
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document.write( "I really have no clue even where to start by solving this problem, I have searched it and found that we need to maximize the area by using a formula that looks something like(2wx2L=?) but after applying it to my problem I came up with this formula (2Lx3W=10,000.  I have no clue if I am even going in the right direction. I used the two lengths because we have two long sides, and 3 widths because there is also the dividing line of fence that has to be accounted for. Any help is appreciated.\r<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "Kim </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127007 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=127007\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A farmer with 10,000 meters of fencing wants to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. What is the largest area that can be enclosed? <BR>\n" );
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document.write( "Draw the picture; there are 3 equal segments of fence (call them \"x\")<BR>\n" );
document.write( "That leaves (10,000-3x) to divide between the two remaining sides;<BR>\n" );
document.write( "so each of them is (10,000-3x)/2 meters = (5000-(3/2)x) meters.<BR>\n" );
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document.write( "EQUATION:<BR>\n" );
document.write( "Area = x(5000-(3/2)x) = 5000x - (3/2)x^2<BR>\n" );
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document.write( "maximum occurs when x = -b/2a = -5000/[2(-3/2)] = 5000/3<BR>\n" );
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document.write( "Area when x = 5000/3 is as follows:\r<BR>\n" );
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document.write( "A(5000/3) = 5000(5000/3) - (3/2) (5000/3)^2 <BR>\n" );
document.write( "= [(5000/3][5000 - (3/2)(5000/3)]\r<BR>\n" );
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document.write( "= [5000/3][2500]<BR>\n" );
document.write( "= 4,166,666.67 sq. meters\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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