document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=808175>Question 808175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For a building at Hertiage college , an architect wants to layout a rectangle piece of ground that has a perimeter of 204 metres and area of 2565 metres squared .Find the dimensions of the ground.\r<BR>\n" );
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document.write( "Can you please help me out? Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #486832 by </B><A HREF=/tutors/aboutme.mpl?userid=JBarnum><B>JBarnum(2146)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JBarnum><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=JBarnum><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=486832\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> length times width equals area<BR>\n" );
document.write( "length plus length plus width plus width equals perimeter<BR>\n" );
document.write( "so:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LW=A ALIGN=MIDDLE  ALT=\"LW=A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L%2B2W=P ALIGN=MIDDLE  ALT=\"2L%2B2W=P\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28L%2BW%29=P ALIGN=MIDDLE  ALT=\"2%28L%2BW%29=P\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2565 ALIGN=MIDDLE  ALT=\"A=2565\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=204 ALIGN=MIDDLE  ALT=\"P=204\"   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=LW=2565 ALIGN=MIDDLE  ALT=\"LW=2565\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "AND<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28L%2BW%29=204 ALIGN=MIDDLE  ALT=\"2%28L%2BW%29=204\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L%2BW%29=102 ALIGN=MIDDLE  ALT=\"%28L%2BW%29=102\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=102-W ALIGN=MIDDLE  ALT=\"L=102-W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "USE ABOVE IN FIRST EQUATION<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28102-W%29W=2565 ALIGN=MIDDLE  ALT=\"%28102-W%29W=2565\"   DISABLED_style= \"max-width:90%; height:auto;\" > DISTRIBUTE<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-W%5E2%2B102W=2565 ALIGN=MIDDLE  ALT=\"-W%5E2%2B102W=2565\"   DISABLED_style= \"max-width:90%; height:auto;\" > PUT IN QUADRATIC FORM AND MULTIPLY BY -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5E2-102W%2B2565=0 ALIGN=MIDDLE  ALT=\"W%5E2-102W%2B2565=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><TABLE  BORDER=1>\n" );
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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=aW%5E2%2BbW%2Bc=0 ALIGN=MIDDLE  ALT=\"aW%5E2%2BbW%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1W%5E2%2B-102W%2B2565+=+0 ALIGN=MIDDLE  ALT=\"1W%5E2%2B-102W%2B2565+=+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=W%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"W%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=%28-102%29%5E2-4%2A1%2A2565=144 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-102%29%5E2-4%2A1%2A2565=144\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=144 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--102%2B-sqrt%28+144+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--102%2B-sqrt%28+144+%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=W%5B1%5D+=+%28-%28-102%29%2Bsqrt%28+144+%29%29%2F2%5C1+=+57 ALIGN=MIDDLE  ALT=\"W%5B1%5D+=+%28-%28-102%29%2Bsqrt%28+144+%29%29%2F2%5C1+=+57\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5B2%5D+=+%28-%28-102%29-sqrt%28+144+%29%29%2F2%5C1+=+45 ALIGN=MIDDLE  ALT=\"W%5B2%5D+=+%28-%28-102%29-sqrt%28+144+%29%29%2F2%5C1+=+45\"   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=1W%5E2%2B-102W%2B2565 ALIGN=MIDDLE  ALT=\"1W%5E2%2B-102W%2B2565\"   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=1W%5E2%2B-102W%2B2565+=+1%28W-57%29%2A%28W-45%29 ALIGN=MIDDLE  ALT=\"1W%5E2%2B-102W%2B2565+=+1%28W-57%29%2A%28W-45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 57, 45.\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-102%2Ax%2B2565+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-102%2Ax%2B2565+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=57 ALIGN=MIDDLE  ALT=\"W=57\"   DISABLED_style= \"max-width:90%; height:auto;\" >OR<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=45 ALIGN=MIDDLE  ALT=\"W=45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "IF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=57 ALIGN=MIDDLE  ALT=\"W=57\"   DISABLED_style= \"max-width:90%; height:auto;\" > THEN <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=102-57 ALIGN=MIDDLE  ALT=\"L=102-57\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=45 ALIGN=MIDDLE  ALT=\"L=45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "IF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=45 ALIGN=MIDDLE  ALT=\"W=45\"   DISABLED_style= \"max-width:90%; height:auto;\" > THEN <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=102-45 ALIGN=MIDDLE  ALT=\"L=102-45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=57 ALIGN=MIDDLE  ALT=\"L=57\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "CHECK <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2A57=2565 ALIGN=MIDDLE  ALT=\"45%2A57=2565\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2B45%2B57%2B57=204 ALIGN=MIDDLE  ALT=\"45%2B45%2B57%2B57=204\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "SINCE LENGTH IS TYPICALLY A GREATER NUMBER THEN THE WIDTH ID GO WITH <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28L=57%29 ALIGN=MIDDLE  ALT=\"highlight%28L=57%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28W=45%29 ALIGN=MIDDLE  ALT=\"highlight%28W=45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );