document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=239763>Question 239763</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a farmer has 100 meters of fence to enclose the maximum area possible. she wishes to use a river bank as a natural boundary for one side of the rectangular garden that she desires to construct. some of the fence will also be used to divide the rectangular into 4 equal rectangular sections\r<BR>\n" );
document.write( "\n" );
document.write( "a)what is the maximum area that cna be enclosed<BR>\n" );
document.write( "b) what dimensions, lenght and widht , produce the maximum area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175879 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=175879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A square give you the most area for the same perimeter.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If the rectangle is composed of 4 squares than it should provide the maximum area because the overall area is equal to the sum of the individual areas.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "consider:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x * x = x^2<BR>\n" );
document.write( "x + x = 2x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Subtract 1 from the left x and add 1 to the right x and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x-1) * (x+1) = x^2 - 1<BR>\n" );
document.write( "(x-1) + (x+1) = 2x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "perimeter remains the same but the area is reduced by 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Subtract 2 from the left x and add 2 to the right x and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x-2) * (x+2) = x^2 - 4<BR>\n" );
document.write( "(x-2) + (x+2) = 2x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Perimeter remains the same but the area is reduced by 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Square is the maximum area for the same perimeter.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "She has 100 meters of fence.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "She will need 4 squares.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That's a total of 16 sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4 of those sides are on the river bank so she can subtract 4 sides from the requirement to get 12 sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "6 of those sides are inside the perimeter of the large rectangle so that 2 sides can be collapsed into 1.  This reduces the number of sides required by another 3 making the total number of sides required equal to 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "100 meters of fence divided by 9 equals 11.111111111 meters per side.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The exact measurement for each side is (100/9).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "With each side measuring (100/9), then the area of each of the squares will be (100/9)^2 = (10000/81)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4 * (10000/81) = (40000/81) = 493.8271605 square meters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "her fence will look like this:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "\r\n" );
document.write( "                       ---- ---- ---- ----\r\n" );
document.write( "                      |    |    |    |    |\r\n" );
document.write( "                      |    |    |    |    |\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That's 9 sides of (100/9) meters each consuming all of the 100 meters of fence.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );