document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=854764>Question 854764</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rope is square root 50 units long. The rope is cut into two pieces, so that the lengths of the pieces are in the ratio 2:3. What is the length of the longer piece expressed in simplest radical form? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #514905 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=514905\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We are given \"A rope is square root 50 units long\", so the rope is 5*sqrt(2) units long.<BR>\n" );
document.write( "let x be one length and y is the other, we know<BR>\n" );
document.write( "x + y = 5*sqrt(2)<BR>\n" );
document.write( "x/y = 2/3<BR>\n" );
document.write( "solve second equation for x<BR>\n" );
document.write( "x = 2y/3<BR>\n" );
document.write( "substitute for x in first equation<BR>\n" );
document.write( "2y/3 +y = 5*sqrt(2)<BR>\n" );
document.write( "multiply both sides of = by 3<BR>\n" );
document.write( "2y +3y = 15*sqrt(2)<BR>\n" );
document.write( "5y = 15*sqrt(2)<BR>\n" );
document.write( "y = 3*sqrt(2)<BR>\n" );
document.write( "x = 2 * 3*sqrt(2) / 3 = 2*sqrt(2) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );