document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=34647>Question 34647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a rope is to be strung from the tops of two posts of heights 10 feet and 8 feet that are 24 feet apart.  The rope needs to be staked to the ground between the two posts.  What is the shortest rope that can possibly be used?  How far from the taller post should it be staked? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #20920 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=20920\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> LET THE 2 POLES BE AB AND CD WITH A AND C ON GROUND<BR>\n" );
document.write( "AB=10.....CD=8.......AC=24....LET THE STAKE POINT BE P ON THE<BR>\n" );
document.write( "GROUND....LET AP=X...SO....PC=24-X<BR>\n" );
document.write( "LENGTH OF ROPE=L=BP+PD.<BR>\n" );
document.write( "L=SQRT{AB^2+BP^2}+SQRT{CD^2+PC^2}.....<BR>\n" );
document.write( "L=SQRT{(100+X^2)+SQRT{64+(24-X)^2}<BR>\n" );
document.write( "DL/DX=0.5*2X/(100+X^2)^(0.5)+0.5*2*(-1)(24-X)/{64+(24-X)^2}^(0.5)=0.<BR>\n" );
document.write( "FOR MINIMUM L...... DL/DX=0....SO<BR>\n" );
document.write( "X/(100+X^2)^0.5=(24-X)/{64+(24-X)^2}^0.5....SQUARING AND CROSS<BR>\n" );
document.write( "MULTIPLYING WE GET<BR>\n" );
document.write( "X^2{64+(24-X)^2}=(24-X)^2(100+X^2)<BR>\n" );
document.write( "64X^2=100(24-X)^2....TAKING SQUARE ROOT<BR>\n" );
document.write( "10(24-X)=+8X.....OR........-8X<BR>\n" );
document.write( "240-10X=8X<BR>\n" );
document.write( "18X=240<BR>\n" );
document.write( "X=40/3..........................I<BR>\n" );
document.write( "IF WE TAKE -8X...THEN<BR>\n" );
document.write( "240-10X=-8X<BR>\n" );
document.write( "2X=240<BR>\n" );
document.write( "X=120...THIS IS NOT POSSIBLE INCE AC=24 ONLY AND X CANT BE MORE THAN THAT<BR>\n" );
document.write( "SO<BR>\n" );
document.write( "X=40/3...IS THE STAKE POINT FROM LONGER POLE...AB<BR>\n" );
document.write( "MINIMUM LENGTH OF ROPE =PUT X=40/3 IN<BR>\n" );
document.write( "L=SQRT{(100+X^2)+SQRT{64+(24-X)^2}=30 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );