document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178858>Question 1178858</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The hypotenuse of a right triangle<BR>\n" );
document.write( "is 3cm longer than one of its legs<BR>\n" );
document.write( "and 6cm longer than its other leg.<BR>\n" );
document.write( "What is the area 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 #808293 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=808293\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the length of the hypotenuse<BR>\n" );
document.write( "Then one of the legs is x-3 and the other leg is x-6<BR>\n" );
document.write( "Since the triangle is a right triangle, using the Pythagorean theorem we have:<BR>\n" );
document.write( "(x-3)^2 + (x-6)^2 = x^2 -> x^2 - 18x + 45 = 0<BR>\n" );
document.write( "This can be factored as:<BR>\n" );
document.write( "(x-3)(x-15) = 0<BR>\n" );
document.write( "The solutions are x = 3 and x = 15. The answer cannot be x = 3, since that would<BR>\n" );
document.write( "make the legs 0 and -3.<BR>\n" );
document.write( "Thus, x = 15. Therefore the area is 1/2*(12)(9) = 54 cm^2 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );