document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=811291>Question 811291</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,<BR>\n" );
document.write( "\"A gardener has 100m of fencing. He must use this to build the biggest fence possible (in square meters).There are 3 sides to the garden bed, attached to the wall which does not require fencing. What are the three side lengths you would use to get the biggest area of fencing?\"\r<BR>\n" );
document.write( "\n" );
document.write( "I know the answer is 50, 25, 25. But how do you develop an equation to solve this for full marks?\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #488676 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=488676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Three sides are in lengths x, y, and y.  <BR>\n" );
document.write( "Two equations are possible.<BR>\n" );
document.write( "Area, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=xy ALIGN=MIDDLE  ALT=\"A=xy\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and fence length, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2By=100 ALIGN=MIDDLE  ALT=\"x%2By%2By=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The biggest area A is wanted.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The fence length equation is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y=100 ALIGN=MIDDLE  ALT=\"x%2B2y=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and we can solve for either variable and substitute into the A equation.  Try <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=100-2y ALIGN=MIDDLE  ALT=\"x=100-2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=xy=%28100-2y%29y ALIGN=MIDDLE  ALT=\"A=xy=%28100-2y%29y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=100y-2y%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28A=100y-2y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That is a parabola with a maximum value.  <BR>\n" );
document.write( "Easiest to find the roots of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100y-2y%5E2=0 ALIGN=MIDDLE  ALT=\"100y-2y%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2850-y%29=0 ALIGN=MIDDLE  ALT=\"2y%2850-y%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=50 ALIGN=MIDDLE  ALT=\"y=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so right in between is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=25 ALIGN=MIDDLE  ALT=\"y=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  That is where A is maximum. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );