document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091801>Question 1091801</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One leg of a right triangle has a length of 11 and all sides are whole numbers. Find the lengths of the other two sides and the hypotenuse? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #706312 by </B><A HREF=/tutors/aboutme.mpl?userid=jorel1380><B>jorel1380(3719)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jorel1380><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=jorel1380><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=706312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We can use the formulas a = x 2 – y 2, b = 2xy, c = x 2 + y 2 to answer this question. Let the legs of the right triangle be a and b and the hypothenus be c, then by the pythagoras theorem<BR>\n" );
document.write( "a^2+b^2=c^2\r<BR>\n" );
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document.write( "Given that<BR>\n" );
document.write( "a =x^2-y^2\r<BR>\n" );
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document.write( "Let a = 11, then<BR>\n" );
document.write( "x^2-y^2=11\r<BR>\n" );
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document.write( "By trial and error, we can find that the value of x = 6 and the value of y = 5.<BR>\n" );
document.write( "i.e.<BR>\n" );
document.write( "x^2-y^2=6^2-5^2=36-25=11\r<BR>\n" );
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document.write( "Thus,<BR>\n" );
document.write( "b = 2(6)(5) = 60<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x^2+y^2=6^2+5^2=36+25=61<BR>\n" );
document.write( "Therefore, the other leg = 60 and the hypotenuse = 61.<BR>\n" );
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