document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166492>Question 166492</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this problem.\r<BR>\n" );
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document.write( "the area of a triangle is 13.5 meters. Find the base and height of the retangle <BR>\n" );
document.write( "if its height is 6 meters greaster than it's base. Use an equation and the formula    area of a triangle =0.5(base)(height). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122696 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=122696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the area of a triangle is 13.5 meters. Find the base and height of the retangle<BR>\n" );
document.write( "if its height is 6 meters greater than it's base. Use an equation and the formula area of a triangle =0.5(base)(height).<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let b = length of the base<BR>\n" );
document.write( "then because \"its height is 6 meters greater than it's base\"<BR>\n" );
document.write( "b+6 = height<BR>\n" );
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document.write( "Plug the above into:<BR>\n" );
document.write( "area of a triangle =0.5(base)(height)<BR>\n" );
document.write( "13.6 =0.5(b)(b+6)<BR>\n" );
document.write( "27.2 =(b)(b+6)<BR>\n" );
document.write( "27.2 = b^2 + 6b<BR>\n" );
document.write( "0 = b^2 + 6b - 27.2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Using the quadratic equation to solve we get:<BR>\n" );
document.write( "b = {3.01664358259653, -9.01664358259653}<BR>\n" );
document.write( "Throw out the neg solution.<BR>\n" );
document.write( "b = 3 meters (base)<BR>\n" );
document.write( "b+6 = 9 meters (height)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Quadratic solved here:<BR>\n" );
document.write( "<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=ab%5E2%2Bbb%2Bc=0 ALIGN=MIDDLE  ALT=\"ab%5E2%2Bbb%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1b%5E2%2B6b%2B-27.2+=+0 ALIGN=MIDDLE  ALT=\"1b%5E2%2B6b%2B-27.2+=+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=b%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"b%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=%286%29%5E2-4%2A1%2A-27.2=144.8 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%286%29%5E2-4%2A1%2A-27.2=144.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=144.8 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+=+%28-6%2B-sqrt%28+144.8+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-6%2B-sqrt%28+144.8+%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=b%5B1%5D+=+%28-%286%29%2Bsqrt%28+144.8+%29%29%2F2%5C1+=+3.01664358259653 ALIGN=MIDDLE  ALT=\"b%5B1%5D+=+%28-%286%29%2Bsqrt%28+144.8+%29%29%2F2%5C1+=+3.01664358259653\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B2%5D+=+%28-%286%29-sqrt%28+144.8+%29%29%2F2%5C1+=+-9.01664358259653 ALIGN=MIDDLE  ALT=\"b%5B2%5D+=+%28-%286%29-sqrt%28+144.8+%29%29%2F2%5C1+=+-9.01664358259653\"   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=1b%5E2%2B6b%2B-27.2 ALIGN=MIDDLE  ALT=\"1b%5E2%2B6b%2B-27.2\"   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=1b%5E2%2B6b%2B-27.2+=+1%28b-3.01664358259653%29%2A%28b--9.01664358259653%29 ALIGN=MIDDLE  ALT=\"1b%5E2%2B6b%2B-27.2+=+1%28b-3.01664358259653%29%2A%28b--9.01664358259653%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3.01664358259653, -9.01664358259653.\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%2B6%2Ax%2B-27.2+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-27.2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );