document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=950228>Question 950228</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a triangle is 140 square feet.If the height is 7 more than the base, find the length of the height and 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 #580217 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=580217\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The area of a triangle is 140 square feet.If the height is 7 more than the base, find the length of the height and base of the triangle. <BR>\n" );
document.write( "b=base; h=heught=b+7; a=1/2bh<BR>\n" );
document.write( "a=1/2bh<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140+sq+ft=1%2F2bh ALIGN=MIDDLE  ALT=\"140+sq+ft=1%2F2bh\"   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=280+sq+ft=bh ALIGN=MIDDLE  ALT=\"280+sq+ft=bh\"   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=280+sq+ft=b%28b%2B7%29 ALIGN=MIDDLE  ALT=\"280+sq+ft=b%28b%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=280+sq+ft=b%5E2%2B7b ALIGN=MIDDLE  ALT=\"280+sq+ft=b%5E2%2B7b\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 280 sq ft from each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=b%5E2%2B7b-280+sq+ft ALIGN=MIDDLE  ALT=\"0=b%5E2%2B7b-280+sq+ft\"   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=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%2B7b%2B-280+=+0 ALIGN=MIDDLE  ALT=\"1b%5E2%2B7b%2B-280+=+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=%287%29%5E2-4%2A1%2A-280=1169 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%287%29%5E2-4%2A1%2A-280=1169\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1169 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+1169+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-7%2B-sqrt%28+1169+%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-%287%29%2Bsqrt%28+1169+%29%29%2F2%5C1+=+13.5953209972788 ALIGN=MIDDLE  ALT=\"b%5B1%5D+=+%28-%287%29%2Bsqrt%28+1169+%29%29%2F2%5C1+=+13.5953209972788\"   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-%287%29-sqrt%28+1169+%29%29%2F2%5C1+=+-20.5953209972788 ALIGN=MIDDLE  ALT=\"b%5B2%5D+=+%28-%287%29-sqrt%28+1169+%29%29%2F2%5C1+=+-20.5953209972788\"   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%2B7b%2B-280 ALIGN=MIDDLE  ALT=\"1b%5E2%2B7b%2B-280\"   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%2B7b%2B-280+=+1%28b-13.5953209972788%29%2A%28b--20.5953209972788%29 ALIGN=MIDDLE  ALT=\"1b%5E2%2B7b%2B-280+=+1%28b-13.5953209972788%29%2A%28b--20.5953209972788%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 13.5953209972788, -20.5953209972788.\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%2B7%2Ax%2B-280+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B-280+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "b=13.595 feet<BR>\n" );
document.write( "h=b+7=13.595+7=20.595<BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "a=1/2bh<BR>\n" );
document.write( "280 sq ft=1/2(13.595)(20.595)<BR>\n" );
document.write( "280 sq ft=280 sq ft </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );