document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=3405>Question 3405</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help:\r<BR>\n" );
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document.write( "Sue wants to put a rectangular garden on her property using 80 meters of fencing.  There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the rectangle.  Fencing is then needed only on the other three sides.)  Let x represent the length of the side of the rectangle along the river.  Express the gardens area as a function of x.  Find the dimensions of the field so that its area is a maximum. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1485 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=1485\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Let the three sides be y, x and y <BR>\n" );
document.write( " Sum of the three sides x + 2y = 80 , so y = (80-x)/2<BR>\n" );
document.write( " Area of the rectangle A = xy = x(80-x)/2 = 40x -x^2/2<BR>\n" );
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document.write( " By complete square A = -1/2(x^2 - 80x + (80/2)^2) + 1600/2<BR>\n" );
document.write( "  = -1/2(x - 40)^2 + 800<BR>\n" );
document.write( " Since (x - 40)^2 >=0,   -1/2(x - 40)^2 <= 0,<BR>\n" );
document.write( " A = -1/2(x - 40)^2 + 800 <= 800,<BR>\n" );
document.write( " when x = 40, y = (80-40)/2 = 20.\r<BR>\n" );
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document.write( " Hence, when the dimensions of the field are 20,40 and 20 meters<BR>\n" );
document.write( "  the max area is 800 sq. meters.\r<BR>\n" );
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document.write( " Kenny<BR>\n" );
document.write( " PS. Also, try to get rid of some redunant words which are not<BR>\n" );
document.write( "     related to math in this question. Like :<BR>\n" );
document.write( "  There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the rectangle. </SPAN>\n" );
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