document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=921124>Question 921124</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a rectangle is 66m^2, and the length of the rectangle is 7m less than three times the width. Find the dimesions of the rectangle?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558756 by </B><A HREF=/tutors/aboutme.mpl?userid=srinivas.g><B>srinivas.g(540)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=srinivas.g><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=srinivas.g><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=558756\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> area  = 66 m^2<BR>\n" );
document.write( "let x,y be the length and width of rectangle <BR>\n" );
document.write( " as per the data  x = 3*y-7<BR>\n" );
document.write( "   But area X*Y   =66 m^2<BR>\n" );
document.write( "          substitute  x=  3y-7 in above equation<BR>\n" );
document.write( "           (3y-7)*y  = 66<BR>\n" );
document.write( "          3y*y-7*y  =66<BR>\n" );
document.write( "         3y^2 -7y=66<BR>\n" );
document.write( "   subtract 66 on both sides<BR>\n" );
document.write( "     3y^2 -7y-66 =66-66<BR>\n" );
document.write( "      3y^2-7y -66 =0<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=ay%5E2%2Bby%2Bc=0 ALIGN=MIDDLE  ALT=\"ay%5E2%2Bby%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%5E2%2B-7y%2B-66+=+0 ALIGN=MIDDLE  ALT=\"3y%5E2%2B-7y%2B-66+=+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=y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"y%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=%28-7%29%5E2-4%2A3%2A-66=841 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-7%29%5E2-4%2A3%2A-66=841\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=841 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--7%2B-sqrt%28+841+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--7%2B-sqrt%28+841+%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=y%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+841+%29%29%2F2%5C3+=+6 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+841+%29%29%2F2%5C3+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+%28-%28-7%29-sqrt%28+841+%29%29%2F2%5C3+=+-3.66666666666667 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+%28-%28-7%29-sqrt%28+841+%29%29%2F2%5C3+=+-3.66666666666667\"   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=3y%5E2%2B-7y%2B-66 ALIGN=MIDDLE  ALT=\"3y%5E2%2B-7y%2B-66\"   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=3y%5E2%2B-7y%2B-66+=+3%28y-6%29%2A%28y--3.66666666666667%29 ALIGN=MIDDLE  ALT=\"3y%5E2%2B-7y%2B-66+=+3%28y-6%29%2A%28y--3.66666666666667%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6, -3.66666666666667.\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+3%2Ax%5E2%2B-7%2Ax%2B-66+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-7%2Ax%2B-66+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "   But Y cannot be negative <BR>\n" );
document.write( "  hence  y =6<BR>\n" );
document.write( "    x= 3*6-7<BR>\n" );
document.write( "      =18-7<BR>\n" );
document.write( "      =11<BR>\n" );
document.write( "length  = 11  m<BR>\n" );
document.write( " width   = 6 m </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );