document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1010866>Question 1010866</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of the longer leg of a right triangle is <BR>\n" );
document.write( "4m<BR>\n" );
document.write( " more than twice the length of the shorter leg. The length of the hypotenuse is <BR>\n" );
document.write( "6m<BR>\n" );
document.write( " more than twice the length of the shorter leg. Find the side lengths 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 #626339 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=626339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call the length of the shorter leg, x.<BR>\n" );
document.write( "Then the longer leg is 2x + 4m.<BR>\n" );
document.write( "The hypotenuse is 2x + 6m.<BR>\n" );
document.write( "By the Pythagorean Theorem, we have<BR>\n" );
document.write( "a^2 + b^2 = c^2<BR>\n" );
document.write( "x^2 + (2x + 4m)^2 = (2x + 6m)^2<BR>\n" );
document.write( "x^2 + 4x^2 + 16xm + 16m^2 = 4x^2 + 24xm + 36m^2<BR>\n" );
document.write( "Now collect like terms and get<BR>\n" );
document.write( "x^2 - 8xm - 20m^2 <BR>\n" );
document.write( "We can factor this into<BR>\n" );
document.write( "(x - 10m)(x + 2m) = 0<BR>\n" );
document.write( "so that<BR>\n" );
document.write( "x = 10m  or  x = -2m<BR>\n" );
document.write( "If we assume m is positive, the solution must be x = 10m.<BR>\n" );
document.write( "Then the other sides are<BR>\n" );
document.write( "24m and 26m. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );