document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=762657>Question 762657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 1200 square foot rectangular garden is enclosed with 150 ft of fencing. Find the dimensions of the garden to two decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464115 by </B><A HREF=/tutors/aboutme.mpl?userid=Stitch><B>Stitch(470)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Stitch><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=464115\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation for the area of a rectangle is A=L*W<BR>\n" );
document.write( "The equation for the perimeter of a rectangle is P=2L+2W<BR>\n" );
document.write( "Given: A=1200 & P=150<BR>\n" );
document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200+=+L%2AW%29%29%29%0D%0AEquation+2%3A+%7B%7B%7B150+=+2L+%2B+2W ALIGN=MIDDLE  ALT=\"1200+=+L%2AW%29%29%29%0D%0AEquation+2%3A+%7B%7B%7B150+=+2L+%2B+2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Start by solving equation 2 for one of the variables.<BR>\n" );
document.write( "Equation 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150+=+2L+%2B+2W ALIGN=MIDDLE  ALT=\"150+=+2L+%2B+2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 2L from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150+-+2L+=+2W ALIGN=MIDDLE  ALT=\"150+-+2L+=+2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor out a 2 on the left side of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%2875-L%29+=+2W ALIGN=MIDDLE  ALT=\"2%2A%2875-L%29+=+2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75+-+L+=+W ALIGN=MIDDLE  ALT=\"75+-+L+=+W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now plug (75-L) into equation 1 for W.<BR>\n" );
document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200+=+L%2AW%29%29%29%0D%0A%7B%7B%7B1200+=+L%2A%2875+-+L%29 ALIGN=MIDDLE  ALT=\"1200+=+L%2AW%29%29%29%0D%0A%7B%7B%7B1200+=+L%2A%2875+-+L%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply the L through.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200+=+75L+-+L%5E2 ALIGN=MIDDLE  ALT=\"1200+=+75L+-+L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 1200 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-L%5E2+%2B+75L+-+1200 ALIGN=MIDDLE  ALT=\"0+=+-L%5E2+%2B+75L+-+1200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now you can use the quadratic equation to solve for L.<BR>\n" );
document.write( "<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%2B75L%2B-1200+=+0 ALIGN=MIDDLE  ALT=\"-1L%5E2%2B75L%2B-1200+=+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=%2875%29%5E2-4%2A-1%2A-1200=825 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2875%29%5E2-4%2A-1%2A-1200=825\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=825 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+=+%28-75%2B-sqrt%28+825+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-75%2B-sqrt%28+825+%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-%2875%29%2Bsqrt%28+825+%29%29%2F2%5C-1+=+23.1385933836549 ALIGN=MIDDLE  ALT=\"L%5B1%5D+=+%28-%2875%29%2Bsqrt%28+825+%29%29%2F2%5C-1+=+23.1385933836549\"   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-%2875%29-sqrt%28+825+%29%29%2F2%5C-1+=+51.8614066163451 ALIGN=MIDDLE  ALT=\"L%5B2%5D+=+%28-%2875%29-sqrt%28+825+%29%29%2F2%5C-1+=+51.8614066163451\"   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%2B75L%2B-1200 ALIGN=MIDDLE  ALT=\"-1L%5E2%2B75L%2B-1200\"   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%2B75L%2B-1200+=+-1%28L-23.1385933836549%29%2A%28L-51.8614066163451%29 ALIGN=MIDDLE  ALT=\"-1L%5E2%2B75L%2B-1200+=+-1%28L-23.1385933836549%29%2A%28L-51.8614066163451%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 23.1385933836549, 51.8614066163451.\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%2B75%2Ax%2B-1200+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B75%2Ax%2B-1200+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "You will end up with two values for L.<BR>\n" );
document.write( "L is equal to 23.14 & 51.86<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "Using the values for L, solve for W.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75+-+L+=+W ALIGN=MIDDLE  ALT=\"75+-+L+=+W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75+-+23.14+=+W ALIGN=MIDDLE  ALT=\"75+-+23.14+=+W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2851.86+=+W%29 ALIGN=MIDDLE  ALT=\"highlight%2851.86+=+W%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75+-+51.86+=+W ALIGN=MIDDLE  ALT=\"75+-+51.86+=+W\"   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%2823.14+=+W%29 ALIGN=MIDDLE  ALT=\"highlight_green%2823.14+=+W%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "In other words the length and width can be switched but the dimensions have to be 23.14ft and 51.86ft\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );