document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=238728>Question 238728</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ladder is leaning against a house with its bottom 15 feet from the house. When the bottom of the ladder is pulled 9 feet further away from the house, the upper end slides 13 feet down. How many feet long is the ladder? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175469 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=175469\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A ladder is leaning against a house with its bottom 15 feet from the house.<BR>\n" );
document.write( " When the bottom of the ladder is pulled 9 feet further away from the house, the upper end slides 13 feet down.<BR>\n" );
document.write( "How many feet long is the ladder?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "This is just a pythag problem: a^2 + b^2 = c^2<BR>\n" );
document.write( "Where <BR>\n" );
document.write( "a = height the ladder is on the building<BR>\n" );
document.write( "b = 15'<BR>\n" );
document.write( "c = length of the ladder<BR>\n" );
document.write( "The equation:<BR>\n" );
document.write( "a^2 + 15^2 = c^2<BR>\n" );
document.write( "a^2 + 225 = c^2<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The ladder slips down 13' and out 9' from the building, <BR>\n" );
document.write( "(a-13) = height of the ladder on the building<BR>\n" );
document.write( "b = 15 + 9 = 24'<BR>\n" );
document.write( "c = length of the ladder, (unchanged)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "the new equation:<BR>\n" );
document.write( "(a-13)^2 + 24^2 = c^2<BR>\n" );
document.write( "FOIL, square 24;<BR>\n" );
document.write( "(a^2 - 26a + 169) + 576 = c^2<BR>\n" );
document.write( "a^2 - 26a + 745 = c^2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Both equation = c^2, therefore:<BR>\n" );
document.write( "a^2 + 225 = a^2 - 26a + 745<BR>\n" );
document.write( "0 = a^2 - a^2 - 26a + 745 - 225<BR>\n" );
document.write( "0 = -26a + 520<BR>\n" );
document.write( "+26a = 520<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=520%2F26 ALIGN=MIDDLE  ALT=\"520%2F26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 20 ft, the original height of the ladder on the building<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the length of the ladder (c)<BR>\n" );
document.write( "c^2 = 20^2 + 15^2<BR>\n" );
document.write( "c^2 = 400 + 225<BR>\n" );
document.write( "c^2 = 625<BR>\n" );
document.write( "c = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28625%29 ALIGN=MIDDLE  ALT=\"sqrt%28625%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c = 25 ft is the ladder length<BR>\n" );
document.write( ";<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Check the solution when ladder slips down, ladder length should be the same<BR>\n" );
document.write( "c^2 = (20-13)^2 + (25+9)^2<BR>\n" );
document.write( "c^2 = 7^2 + 24^2 =<BR>\n" );
document.write( "c^2 = 49 + 576<BR>\n" );
document.write( "c^2 = 625<BR>\n" );
document.write( "c = 25'; confirms our solution\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );