document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=957519>Question 957519</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the base of a triangle exceeds twice its altitude by 18m. If the area of the triangle be360 sq.m . What is its altitude?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #585124 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=585124\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A=area=360 sq m; h=altitude; b=base=2h+18m<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%281%2F2%29bh ALIGN=MIDDLE  ALT=\"A=%281%2F2%29bh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute for b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360m%5E2=%281%2F2%29%282h%2B18%29%28h%29 ALIGN=MIDDLE  ALT=\"360m%5E2=%281%2F2%29%282h%2B18%29%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply each side by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720m%5E2=2h%5E2%2B18h ALIGN=MIDDLE  ALT=\"720m%5E2=2h%5E2%2B18h\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 720 m^2 from each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2h%5E2%2B18h-720m%5E2 ALIGN=MIDDLE  ALT=\"0=2h%5E2%2B18h-720m%5E2\"   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=ah%5E2%2Bbh%2Bc=0 ALIGN=MIDDLE  ALT=\"ah%5E2%2Bbh%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2h%5E2%2B18h%2B-720+=+0 ALIGN=MIDDLE  ALT=\"2h%5E2%2B18h%2B-720+=+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=h%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"h%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=%2818%29%5E2-4%2A2%2A-720=6084 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2818%29%5E2-4%2A2%2A-720=6084\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=6084 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+=+%28-18%2B-sqrt%28+6084+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-18%2B-sqrt%28+6084+%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=h%5B1%5D+=+%28-%2818%29%2Bsqrt%28+6084+%29%29%2F2%5C2+=+15 ALIGN=MIDDLE  ALT=\"h%5B1%5D+=+%28-%2818%29%2Bsqrt%28+6084+%29%29%2F2%5C2+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B2%5D+=+%28-%2818%29-sqrt%28+6084+%29%29%2F2%5C2+=+-24 ALIGN=MIDDLE  ALT=\"h%5B2%5D+=+%28-%2818%29-sqrt%28+6084+%29%29%2F2%5C2+=+-24\"   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=2h%5E2%2B18h%2B-720 ALIGN=MIDDLE  ALT=\"2h%5E2%2B18h%2B-720\"   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=2h%5E2%2B18h%2B-720+=+2%28h-15%29%2A%28h--24%29 ALIGN=MIDDLE  ALT=\"2h%5E2%2B18h%2B-720+=+2%28h-15%29%2A%28h--24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 15, -24.\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+2%2Ax%5E2%2B18%2Ax%2B-720+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B18%2Ax%2B-720+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "h=15m ANSWER: The altitude of the triangle is 15 meters.<BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "b=2h+18m=2(15m)+18m=48m The base of the triangle is 48 meters.<BR>\n" );
document.write( "A=1/2bh<BR>\n" );
document.write( "360sq m=1/2(48m)(15m)<BR>\n" );
document.write( "360 sq m=360 sq m </SPAN>\n" );
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