document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=891964>Question 891964</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer wants to enclose a rectangular lot using 50 meters of fencing materials. If he needs an area of at least 50 SQUARE meters, find the range for the possible length of the lot. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #540233 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=540233\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> w for width and L for length;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%2B2L=50 ALIGN=MIDDLE  ALT=\"2w%2B2L=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=wL%3E=50 ALIGN=MIDDLE  ALT=\"wL%3E=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Using first the perimeter equation, w+L=25<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=25-L ALIGN=MIDDLE  ALT=\"w=25-L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825-L%29L%3E=50 ALIGN=MIDDLE  ALT=\"%2825-L%29L%3E=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25L-L%5E2%3E=50 ALIGN=MIDDLE  ALT=\"25L-L%5E2%3E=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-L%5E2%2B25L-50%3E=0 ALIGN=MIDDLE  ALT=\"-L%5E2%2B25L-50%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28L%5E2-25L%2B50%3C=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%28L%5E2-25L%2B50%3C=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "roots for the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%2825%2B-+sqrt%2825%5E2-4%2A50%29%29%2F2 ALIGN=MIDDLE  ALT=\"L=%2825%2B-+sqrt%2825%5E2-4%2A50%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%2825%2B-+sqrt%28425%29%29%2F2 ALIGN=MIDDLE  ALT=\"L=%2825%2B-+sqrt%28425%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%2825%2B-+5%2Asqrt%2817%29%29%2F2 ALIGN=MIDDLE  ALT=\"L=%2825%2B-+5%2Asqrt%2817%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The parabola with L has a minimum based on coefficient on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2 ALIGN=MIDDLE  ALT=\"L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > being a positive 1.  This means that L cannot be between the two roots.  The inequality is satisfied for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280%3CL%3C=%2825-5sqrt%2817%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%280%3CL%3C=%2825-5sqrt%2817%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%2825%2B5sqrt%2817%29%29%2F2%3C=L%3C50%29 ALIGN=MIDDLE  ALT=\"highlight%28%2825%2B5sqrt%2817%29%29%2F2%3C=L%3C50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );