document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=209727>Question 209727</A>: <I><SPAN STYLE=\"word-break: break-all;\"> area of a rectangle is 243 m2. The height is nine less than 4 times the base. What is the perimeter? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #162253 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=162253\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Area of a rectangle is 243 m^2. The height is nine less than 4 times the base. What is the perimeter?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 1.  Let x be the base and 4x-9 be the height\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 2.  Perimeter P means adding up the four sides of a rectangle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 3.  Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=x%2Bx%2B4x-9%2B4x-9=10x-9 ALIGN=MIDDLE  ALT=\"P=x%2Bx%2B4x-9%2B4x-9=10x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 4.  Area=x*(4x-9)=243  or 4x^2-9x-243=0 or a quadratic equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 5.  We can use the quadratic formula given as \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "where a=4, b=-9 and c=-243\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B-9x%2B-243+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-9x%2B-243+=+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=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%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=%28-9%29%5E2-4%2A4%2A-243=3969 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-9%29%5E2-4%2A4%2A-243=3969\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3969 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--9%2B-sqrt%28+3969+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--9%2B-sqrt%28+3969+%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=x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+3969+%29%29%2F2%5C4+=+9 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+3969+%29%29%2F2%5C4+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-9%29-sqrt%28+3969+%29%29%2F2%5C4+=+-6.75 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-9%29-sqrt%28+3969+%29%29%2F2%5C4+=+-6.75\"   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=4x%5E2%2B-9x%2B-243 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-9x%2B-243\"   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=4x%5E2%2B-9x%2B-243+=+4%28x-9%29%2A%28x--6.75%29 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-9x%2B-243+=+4%28x-9%29%2A%28x--6.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 9, -6.75.\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+4%2Ax%5E2%2B-9%2Ax%2B-243+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-9%2Ax%2B-243+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Select the positive number x=9.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 6.  Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=x%2Bx%2B4x-9%2B4x-9=10x-9=10%2A9-9=81 ALIGN=MIDDLE  ALT=\"P=x%2Bx%2B4x-9%2B4x-9=10x-9=10%2A9-9=81\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 7.  ANSWER:  The perimeter is 81.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I just found this problem on 18 Sep 09, but I hope the above steps were helpful for review.  Sorry about the late response.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And good luck in your studies!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Respectfully,<BR>\n" );
document.write( "Dr J </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );