document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=952084>Question 952084</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in a right-angled triangle one right-angled side is 2m longer than the other one. Calculate the length of the two right-angled sides if the area is 48m^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #581482 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=581482\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x=shorter leg (height); x+2m=longer leg (base); Area=1/2(base)(height)<BR>\n" );
document.write( "A=(1/2)(x)(x+2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48m%5E2=%281%2F2%29%28x%5E2%2B2x%29 ALIGN=MIDDLE  ALT=\"48m%5E2=%281%2F2%29%28x%5E2%2B2x%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=96m%5E2=x%5E2%2B2x+Subtract+96m%5E2+from+each+side.%0D%0A%7B%7B%7B0=x%5E2%2B2x-96m%5E2 ALIGN=MIDDLE  ALT=\"96m%5E2=x%5E2%2B2x+Subtract+96m%5E2+from+each+side.%0D%0A%7B%7B%7B0=x%5E2%2B2x-96m%5E2\"   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=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=1x%5E2%2B2x%2B-96+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B2x%2B-96+=+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=%282%29%5E2-4%2A1%2A-96=388 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%282%29%5E2-4%2A1%2A-96=388\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=388 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+388+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-2%2B-sqrt%28+388+%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-%282%29%2Bsqrt%28+388+%29%29%2F2%5C1+=+8.8488578017961 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%282%29%2Bsqrt%28+388+%29%29%2F2%5C1+=+8.8488578017961\"   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-%282%29-sqrt%28+388+%29%29%2F2%5C1+=+-10.8488578017961 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%282%29-sqrt%28+388+%29%29%2F2%5C1+=+-10.8488578017961\"   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=1x%5E2%2B2x%2B-96 ALIGN=MIDDLE  ALT=\"1x%5E2%2B2x%2B-96\"   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=1x%5E2%2B2x%2B-96+=+1%28x-8.8488578017961%29%2A%28x--10.8488578017961%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B2x%2B-96+=+1%28x-8.8488578017961%29%2A%28x--10.8488578017961%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 8.8488578017961, -10.8488578017961.\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%2B2%2Ax%2B-96+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-96+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "ANSWER 1: The shorter side is 8.85 meters.<BR>\n" );
document.write( "x+2=8.85+2=10.85 ANSWER 2: The longer side is 10.85 meters.<BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "a=1/2(b)(h)<BR>\n" );
document.write( "48 sq m=(1/2)(10.85 m)(8.85m)<BR>\n" );
document.write( "48 sq m=48 sq m<BR>\n" );
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document.write( " </SPAN>\n" );
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