document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1053258>Question 1053258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right triangle is 1 foot longer than one of the sides. If the other side was 1 foot longer, it would be exactly one third the length of the first side. Find the length of each of the sides, and of 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 #668514 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=668514\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> hypotenuse=x<BR>\n" );
document.write( "one side is x-1<BR>\n" );
document.write( "the third side is x^2-(x-1)^2, which is sqrt {x^2-(x^2-2x+1)}=sqrt (2x-1).<BR>\n" );
document.write( "adding 1 to the third side makes it sqrt(2x-1)+1=(1/3)(x-1)=(1/3)x-(1/3)<BR>\n" );
document.write( "sqrt(2x-1)=(1/3)x-(4/3)<BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "2x-1=(1/9)x^2-(8/9)x+(16/9)<BR>\n" );
document.write( "0=(1/9)x^2-(26/9)x+(25/9)<BR>\n" );
document.write( "multiply everything by 9<BR>\n" );
document.write( "0=x^2-26x+25<BR>\n" );
document.write( "(x-25)(x-1)=0;<BR>\n" );
document.write( "x=25, 1, and 1 is impossible<BR>\n" );
document.write( "x-1=24<BR>\n" );
document.write( "The third side is 7 (7,24,25 triangle) and 7+1 is 1/3 of 24.\r<BR>\n" );
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