document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982518>Question 982518</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular garden has an area of 84 sq meters and a perimeter of 38 meters. Find its length. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603371 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=603371\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "L=length; W=width; A=Area; P=perimeter<BR>\n" );
document.write( ".<BR>\n" );
document.write( "P=2(L+W)<BR>\n" );
document.write( "38m=2(L+W)<BR>\n" );
document.write( "19m=L+W<BR>\n" );
document.write( "19m-L=W<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A=LW<BR>\n" );
document.write( "84m^2=LW<BR>\n" );
document.write( "84m^2=L(19m-L)<BR>\n" );
document.write( "84m^2=19Lm-L^2<BR>\n" );
document.write( "0=-L^2+19Lm-84m^2<BR>\n" );
document.write( "0=L^2-19Lm+84m^2<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=aL%5E2%2BbL%2Bc=0 ALIGN=MIDDLE  ALT=\"aL%5E2%2BbL%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1L%5E2%2B-19L%2B84+=+0 ALIGN=MIDDLE  ALT=\"1L%5E2%2B-19L%2B84+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"L%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-19%29%5E2-4%2A1%2A84=25 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-19%29%5E2-4%2A1%2A84=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=25 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--19%2B-sqrt%28+25+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--19%2B-sqrt%28+25+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5B1%5D+=+%28-%28-19%29%2Bsqrt%28+25+%29%29%2F2%5C1+=+12 ALIGN=MIDDLE  ALT=\"L%5B1%5D+=+%28-%28-19%29%2Bsqrt%28+25+%29%29%2F2%5C1+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5B2%5D+=+%28-%28-19%29-sqrt%28+25+%29%29%2F2%5C1+=+7 ALIGN=MIDDLE  ALT=\"L%5B2%5D+=+%28-%28-19%29-sqrt%28+25+%29%29%2F2%5C1+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1L%5E2%2B-19L%2B84 ALIGN=MIDDLE  ALT=\"1L%5E2%2B-19L%2B84\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1L%5E2%2B-19L%2B84+=+1%28L-12%29%2A%28L-7%29 ALIGN=MIDDLE  ALT=\"1L%5E2%2B-19L%2B84+=+1%28L-12%29%2A%28L-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 12, 7.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-19%2Ax%2B84+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-19%2Ax%2B84+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "Length is 12 meters or 7 meters <BR>\n" );
document.write( "(If length is 12m, width is 7m, if length is 7m width is 12m) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );