document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=951622>Question 951622</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a triangular sheet of paper is 185 square inches. One side of the triangle is 7 inches more than three times the length of the altitude to that side. Find the length of that side and the altitude to the side.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #581384 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=581384\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> b=side; h=altitude; A=Area=(1/2)b*h<BR>\n" );
document.write( "A=(1/2)b*h<BR>\n" );
document.write( "185 sq in=(1/2)(3h+7in)(h) Multiply each side by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=370+sq+in=3h%5E2%2B7h ALIGN=MIDDLE  ALT=\"370+sq+in=3h%5E2%2B7h\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 370 sq in from each side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=3h%5E2%2B7h-370+sq+in ALIGN=MIDDLE  ALT=\"0=3h%5E2%2B7h-370+sq+in\"   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=3h%5E2%2B7h%2B-370+=+0 ALIGN=MIDDLE  ALT=\"3h%5E2%2B7h%2B-370+=+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=%287%29%5E2-4%2A3%2A-370=4489 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%287%29%5E2-4%2A3%2A-370=4489\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=4489 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+=+%28-7%2B-sqrt%28+4489+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-7%2B-sqrt%28+4489+%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-%287%29%2Bsqrt%28+4489+%29%29%2F2%5C3+=+10 ALIGN=MIDDLE  ALT=\"h%5B1%5D+=+%28-%287%29%2Bsqrt%28+4489+%29%29%2F2%5C3+=+10\"   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-%287%29-sqrt%28+4489+%29%29%2F2%5C3+=+-12.3333333333333 ALIGN=MIDDLE  ALT=\"h%5B2%5D+=+%28-%287%29-sqrt%28+4489+%29%29%2F2%5C3+=+-12.3333333333333\"   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=3h%5E2%2B7h%2B-370 ALIGN=MIDDLE  ALT=\"3h%5E2%2B7h%2B-370\"   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=3h%5E2%2B7h%2B-370+=+3%28h-10%29%2A%28h--12.3333333333333%29 ALIGN=MIDDLE  ALT=\"3h%5E2%2B7h%2B-370+=+3%28h-10%29%2A%28h--12.3333333333333%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 10, -12.3333333333333.\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%2B7%2Ax%2B-370+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B7%2Ax%2B-370+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "ANSWER 1: Length of the altitude is 10 inches<BR>\n" );
document.write( "b=3h+7in=3(10in)+7in=37 in ANSWER 2: The length of the side is 37 inches.<BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "Area=1/2bh=1/2(37 in)(10 in)<BR>\n" );
document.write( "185 sq in=1/2(370 sq in)<BR>\n" );
document.write( "185 sq in=185 sq in<BR>\n" );
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