document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=709684>Question 709684</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the base and height of a triangle are (x+3)cm and (2x+5)cm respectively if the area of a triangle is 20 cm square , find x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436739 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=436739\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the base and height of a triangle are (x+3)cm and (2x+5)cm respectively if the area of a triangle is 20 cm square , find x<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since area of a triangle is:<BR>\n" );
document.write( "(1/2)bh = area<BR>\n" );
document.write( "plugging in the given data:<BR>\n" );
document.write( "(1/2)(x+3)(2x+5) = 20<BR>\n" );
document.write( "multiplying both sides by 2:<BR>\n" );
document.write( "(x+3)(2x+5) = 40<BR>\n" );
document.write( "FOIL the left:<BR>\n" );
document.write( "2x^2+5x+6x+15 = 40<BR>\n" );
document.write( "2x^2+11x+15 = 40<BR>\n" );
document.write( "2x^2+11x-25 = 0<BR>\n" );
document.write( "applying the \"quadratic equation\" we get:<BR>\n" );
document.write( "x = {1.73, -7.23}<BR>\n" );
document.write( ".<BR>\n" );
document.write( "details of quadratic follows:<BR>\n" );
document.write( "<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=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=2x%5E2%2B11x%2B-25+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B11x%2B-25+=+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" );
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=%2811%29%5E2-4%2A2%2A-25=321 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2811%29%5E2-4%2A2%2A-25=321\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=321 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+=+%28-11%2B-sqrt%28+321+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-11%2B-sqrt%28+321+%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-%2811%29%2Bsqrt%28+321+%29%29%2F2%5C2+=+1.72911821679223 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2811%29%2Bsqrt%28+321+%29%29%2F2%5C2+=+1.72911821679223\"   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-%2811%29-sqrt%28+321+%29%29%2F2%5C2+=+-7.22911821679223 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2811%29-sqrt%28+321+%29%29%2F2%5C2+=+-7.22911821679223\"   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=2x%5E2%2B11x%2B-25 ALIGN=MIDDLE  ALT=\"2x%5E2%2B11x%2B-25\"   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=2x%5E2%2B11x%2B-25+=+2%28x-1.72911821679223%29%2A%28x--7.22911821679223%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B11x%2B-25+=+2%28x-1.72911821679223%29%2A%28x--7.22911821679223%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.72911821679223, -7.22911821679223.\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%2B11%2Ax%2B-25+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B11%2Ax%2B-25+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );