document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=636954>Question 636954</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The hypotenuse of right triangle is  twice as long as one of the legs and eight inches longer than the other What are the lengths of the sides of the triangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401321 by </B><A HREF=/tutors/aboutme.mpl?userid=graphmatics><B>graphmatics(170)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=graphmatics><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=graphmatics><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=401321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let a and b be the sides of the right triangle and c be the hypotenuse. We are given that:<BR>\n" );
document.write( "c=2*a<BR>\n" );
document.write( "c=b+8<BR>\n" );
document.write( "Being a right triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ",putting each of the expressions for c into this equation we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Aa%29%5E2=4%2Aa%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%282%2Aa%29%5E2=4%2Aa%5E2=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2B8%29%5E2=b%5E2%2B16%2Ab%2B64=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28b%2B8%29%5E2=b%5E2%2B16%2Ab%2B64=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From equation one we get that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=b%5E2%2F3 ALIGN=MIDDLE  ALT=\"a%5E2=b%5E2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Put this into equation two:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2B16%2Ab%2B64=b%5E2%2F3%2Bb%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2B16%2Ab%2B64=b%5E2%2F3%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-48%2Ab-192=0 ALIGN=MIDDLE  ALT=\"b%5E2-48%2Ab-192=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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%2B-48b%2B-192+=+0 ALIGN=MIDDLE  ALT=\"1b%5E2%2B-48b%2B-192+=+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=%28-48%29%5E2-4%2A1%2A-192=3072 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-48%29%5E2-4%2A1%2A-192=3072\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3072 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--48%2B-sqrt%28+3072+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--48%2B-sqrt%28+3072+%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-%28-48%29%2Bsqrt%28+3072+%29%29%2F2%5C1+=+51.712812921102 ALIGN=MIDDLE  ALT=\"b%5B1%5D+=+%28-%28-48%29%2Bsqrt%28+3072+%29%29%2F2%5C1+=+51.712812921102\"   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-%28-48%29-sqrt%28+3072+%29%29%2F2%5C1+=+-3.71281292110204 ALIGN=MIDDLE  ALT=\"b%5B2%5D+=+%28-%28-48%29-sqrt%28+3072+%29%29%2F2%5C1+=+-3.71281292110204\"   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%2B-48b%2B-192 ALIGN=MIDDLE  ALT=\"1b%5E2%2B-48b%2B-192\"   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%2B-48b%2B-192+=+1%28b-51.712812921102%29%2A%28b--3.71281292110204%29 ALIGN=MIDDLE  ALT=\"1b%5E2%2B-48b%2B-192+=+1%28b-51.712812921102%29%2A%28b--3.71281292110204%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 51.712812921102, -3.71281292110204.\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%2B-48%2Ax%2B-192+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-48%2Ax%2B-192+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "b=51.71 So c=59.71 a=59,71/2=29.85 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );