document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=954664>Question 954664</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right triangle is 12cm longer than the shortest side, and 6cm longer than the remaining side. Find the dimensions 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 #583157 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=583157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> c=hypotenuse; a=shortest leg=c-12cm; b=longer leg=c-6cm<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute for a and b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c-12cm%29%5E2%2B%28c-6cm%29%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"%28c-12cm%29%5E2%2B%28c-6cm%29%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c%5E2-24c%2B144%29%2B%28c%5E2-12c%2B36%29=c%5E2 ALIGN=MIDDLE  ALT=\"%28c%5E2-24c%2B144%29%2B%28c%5E2-12c%2B36%29=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2c%5E2-36c%2B180=c%5E2 ALIGN=MIDDLE  ALT=\"2c%5E2-36c%2B180=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2 ALIGN=MIDDLE  ALT=\"c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from each side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2-36c%2B180=0 ALIGN=MIDDLE  ALT=\"c%5E2-36c%2B180=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=ac%5E2%2Bbc%2Bc=0 ALIGN=MIDDLE  ALT=\"ac%5E2%2Bbc%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1c%5E2%2B-36c%2B180+=+0 ALIGN=MIDDLE  ALT=\"1c%5E2%2B-36c%2B180+=+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=c%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"c%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=%28-36%29%5E2-4%2A1%2A180=576 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-36%29%5E2-4%2A1%2A180=576\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=576 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--36%2B-sqrt%28+576+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--36%2B-sqrt%28+576+%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=c%5B1%5D+=+%28-%28-36%29%2Bsqrt%28+576+%29%29%2F2%5C1+=+30 ALIGN=MIDDLE  ALT=\"c%5B1%5D+=+%28-%28-36%29%2Bsqrt%28+576+%29%29%2F2%5C1+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5B2%5D+=+%28-%28-36%29-sqrt%28+576+%29%29%2F2%5C1+=+6 ALIGN=MIDDLE  ALT=\"c%5B2%5D+=+%28-%28-36%29-sqrt%28+576+%29%29%2F2%5C1+=+6\"   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=1c%5E2%2B-36c%2B180 ALIGN=MIDDLE  ALT=\"1c%5E2%2B-36c%2B180\"   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=1c%5E2%2B-36c%2B180+=+1%28c-30%29%2A%28c-6%29 ALIGN=MIDDLE  ALT=\"1c%5E2%2B-36c%2B180+=+1%28c-30%29%2A%28c-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 30, 6.\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-36%2Ax%2B180+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-36%2Ax%2B180+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "Possible solutions are 30 and 6 Since a=c-12, 6 doesn't work.<BR>\n" );
document.write( "c=30 cm<BR>\n" );
document.write( "ANSWER 1: The hypotenuse is 30 cm.<BR>\n" );
document.write( "a=c-12cm=30-12cm=18cm<BR>\n" );
document.write( "ANSWER 2: The shortest leg is 18 cm.<BR>\n" );
document.write( "b=c-6cm=30-6cm=24cm<BR>\n" );
document.write( "ANSWER 3: The longer leg is 24 cm.<BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%5E2cm%5E2%2B24%5E2cm%5E2=30%5E2cm%5E2 ALIGN=MIDDLE  ALT=\"18%5E2cm%5E2%2B24%5E2cm%5E2=30%5E2cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=324cm%5E2%2B576cm%5E2=900cm%5E2 ALIGN=MIDDLE  ALT=\"324cm%5E2%2B576cm%5E2=900cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900cm%5E2=900cm%5E2 ALIGN=MIDDLE  ALT=\"900cm%5E2=900cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );