document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964264>Question 964264</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The height of a triangle is 2 centimeters less than its base. If the area of the triangle is 28 square centimeters, find the base and height of the triangle. Round to the nearest tenth of a centimeter if necessary. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589141 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=589141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> b=base; h=height=b-2cm<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 h.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%281%2F2%29%28b%29%28b-2cm%29 ALIGN=MIDDLE  ALT=\"A=%281%2F2%29%28b%29%28b-2cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28cm%5E2=%281%2F2%29%28b%29%28b-2cm%29 ALIGN=MIDDLE  ALT=\"28cm%5E2=%281%2F2%29%28b%29%28b-2cm%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=56cm%5E2=b%5E2-2b ALIGN=MIDDLE  ALT=\"56cm%5E2=b%5E2-2b\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 56 from each side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=b%5E2-2b-56 ALIGN=MIDDLE  ALT=\"0=b%5E2-2b-56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\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=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%2B-2b%2B-56+=+0 ALIGN=MIDDLE  ALT=\"1b%5E2%2B-2b%2B-56+=+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=%28-2%29%5E2-4%2A1%2A-56=228 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-56=228\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=228 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--2%2B-sqrt%28+228+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--2%2B-sqrt%28+228+%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-%28-2%29%2Bsqrt%28+228+%29%29%2F2%5C1+=+8.54983443527075 ALIGN=MIDDLE  ALT=\"b%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+228+%29%29%2F2%5C1+=+8.54983443527075\"   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-%28-2%29-sqrt%28+228+%29%29%2F2%5C1+=+-6.54983443527075 ALIGN=MIDDLE  ALT=\"b%5B2%5D+=+%28-%28-2%29-sqrt%28+228+%29%29%2F2%5C1+=+-6.54983443527075\"   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%2B-2b%2B-56 ALIGN=MIDDLE  ALT=\"1b%5E2%2B-2b%2B-56\"   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%2B-2b%2B-56+=+1%28b-8.54983443527075%29%2A%28b--6.54983443527075%29 ALIGN=MIDDLE  ALT=\"1b%5E2%2B-2b%2B-56+=+1%28b-8.54983443527075%29%2A%28b--6.54983443527075%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 8.54983443527075, -6.54983443527075.\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-2%2Ax%2B-56+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-56+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "ANSWER 1: The base is 8.55 cm. (This would round to 8.5cm- kept extra digit for check)<BR>\n" );
document.write( "h=b-2cm=8.55cm=6.55 cm (see above) <BR>\n" );
document.write( "ANSWER 2: The height is 6.55 cm.<BR>\n" );
document.write( "CHECK:<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28cm%5E2=%281%2F2%29%288.55cm%29%286.55cm%29 ALIGN=MIDDLE  ALT=\"28cm%5E2=%281%2F2%29%288.55cm%29%286.55cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28cm%5E2=%281%2F2%29%2856.00cm%5E2%29 ALIGN=MIDDLE  ALT=\"28cm%5E2=%281%2F2%29%2856.00cm%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28cn%5E2=28cm%5E2 ALIGN=MIDDLE  ALT=\"28cn%5E2=28cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );