document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=600854>Question 600854</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The height of a triangle is 10 inches less than the three times the base. the area is 156 square inches. what is the base of the triangle?<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 #379523 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=379523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The height of a triangle is 10 inches less than the three times the base. the area is 156 square inches. what is the base of the triangle?<BR>\n" );
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document.write( "Let b = base<BR>\n" );
document.write( "then<BR>\n" );
document.write( "3b-10 = height<BR>\n" );
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document.write( "area = (1/2)base*height<BR>\n" );
document.write( "156 = (1/2)b(3b-10)<BR>\n" );
document.write( "312 = b(3b-10)<BR>\n" );
document.write( "312 = 3b^2-10b<BR>\n" );
document.write( "0 = 3b^2-10b-312<BR>\n" );
document.write( "solve using the quadratic formula to get:<BR>\n" );
document.write( "x = {12, -8.67}<BR>\n" );
document.write( "throw out the negative solution leaving<BR>\n" );
document.write( "x = 12 inches<BR>\n" );
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document.write( "details of quadratic formula follows:<BR>\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=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=3x%5E2%2B-10x%2B-312+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-10x%2B-312+=+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" );
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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" );
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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=%28-10%29%5E2-4%2A3%2A-312=3844 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-10%29%5E2-4%2A3%2A-312=3844\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3844 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--10%2B-sqrt%28+3844+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--10%2B-sqrt%28+3844+%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-%28-10%29%2Bsqrt%28+3844+%29%29%2F2%5C3+=+12 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+3844+%29%29%2F2%5C3+=+12\"   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-%28-10%29-sqrt%28+3844+%29%29%2F2%5C3+=+-8.66666666666667 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-10%29-sqrt%28+3844+%29%29%2F2%5C3+=+-8.66666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B-10x%2B-312 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-10x%2B-312\"   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=3x%5E2%2B-10x%2B-312+=+3%28x-12%29%2A%28x--8.66666666666667%29 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-10x%2B-312+=+3%28x-12%29%2A%28x--8.66666666666667%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 12, -8.66666666666667.\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-10%2Ax%2B-312+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-10%2Ax%2B-312+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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