document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246443>Question 246443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> THE HYPOTENUSE OF A RIGHT TRIANGLE IS 1 INCH LONGER THAN ONE LEG AND 8 INCHES LONGER THAN THE OTHER. FIND THE LENGTH OF EACH SIDE 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 #179966 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=179966\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> right triangle<BR>\n" );
document.write( "c^2=a^2+b^2<BR>\n" );
document.write( "where c is the hypotenuse and a and b are the legs.\r<BR>\n" );
document.write( "\n" );
document.write( "c=a+1<BR>\n" );
document.write( "solve for a<BR>\n" );
document.write( "a=c-1<BR>\n" );
document.write( "c=b+8<BR>\n" );
document.write( "solve for b<BR>\n" );
document.write( "b=c-8<BR>\n" );
document.write( "substitute<BR>\n" );
document.write( "c^2=(c-1)^2+(c-8)^2<BR>\n" );
document.write( "(c-1)^2=c^2-2c+1<BR>\n" );
document.write( "(c-8)^2=c^2-16+64<BR>\n" );
document.write( "c^2=2c^2-18c+65<BR>\n" );
document.write( "subtract c^2<BR>\n" );
document.write( "c^2-18c+65=0<BR>\n" );
document.write( "13 and 5<BR>\n" );
document.write( "13,12, 5<BR>\n" );
document.write( "5,4,-3<BR>\n" );
document.write( "but -3 can't be a side of a triangle<BR>\n" );
document.write( "so we have 13, 12, and 5<BR>\n" );
document.write( "13 is hypotenuse<BR>\n" );
document.write( "12 and 5 are the legs\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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=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%2B-18x%2B65+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-18x%2B65+=+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=%28-18%29%5E2-4%2A1%2A65=64 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-18%29%5E2-4%2A1%2A65=64\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=64 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--18%2B-sqrt%28+64+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--18%2B-sqrt%28+64+%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-%28-18%29%2Bsqrt%28+64+%29%29%2F2%5C1+=+13 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-18%29%2Bsqrt%28+64+%29%29%2F2%5C1+=+13\"   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-%28-18%29-sqrt%28+64+%29%29%2F2%5C1+=+5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-18%29-sqrt%28+64+%29%29%2F2%5C1+=+5\"   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%2B-18x%2B65 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-18x%2B65\"   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%2B-18x%2B65+=+1%28x-13%29%2A%28x-5%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-18x%2B65+=+1%28x-13%29%2A%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 13, 5.\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-18%2Ax%2B65+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-18%2Ax%2B65+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );