document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=358130>Question 358130</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ladder leans against a barn with its base 15 feet from the barn. when the ladder is pulled 9 feet further away from the barn, the upper end slides down 13 feet. how long is the ladder?\r<BR>\n" );
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document.write( "So far I have tried the Pythagorean theorem but I am not sure where to plug which numbers into. I also know that the ladder is a total of 24 feet away from the barn. Please help me, thanks so much.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #255626 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=255626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A ladder leans against a barn with its base 15 feet from the barn. when the ladder is pulled 9 feet further away from the barn, the upper end slides down 13 feet. how long is the ladder? <BR>\n" );
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document.write( "The \"ladder\" is always the hypotenuse.<BR>\n" );
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document.write( "Before the slide:<BR>\n" );
document.write( "Let x = height where the ladder hits the barn<BR>\n" );
document.write( "and y = ladder's length<BR>\n" );
document.write( "then<BR>\n" );
document.write( "x^2 + 15^2 = y^2 (equation 1)<BR>\n" );
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document.write( "After the slide:<BR>\n" );
document.write( "(x-9)^2 + (15+9)^2 = y^2<BR>\n" );
document.write( "(x-9)^2 + (24)^2 = y^2 (equation 2)<BR>\n" );
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document.write( "Since equation 1 and equation 2 both defines y^2 we have:<BR>\n" );
document.write( "x^2 + 15^2 = (x-9)^2 + (24)^2<BR>\n" );
document.write( "x^2 + 225 = (x-9)^2 + 576<BR>\n" );
document.write( "x^2 + 225 = (x-9)(x-9) + 576<BR>\n" );
document.write( "x^2 + 225 = (x^2-18x+81) + 576<BR>\n" );
document.write( "x^2 + 225 = x^2-18x+657<BR>\n" );
document.write( "225 = -18x+657<BR>\n" );
document.write( "-432 = -18x<BR>\n" );
document.write( "24 = x<BR>\n" );
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document.write( "To find y (the ladder's length) plug the above back into equation 1 and solve for y:<BR>\n" );
document.write( "x^2 + 15^2 = y^2<BR>\n" );
document.write( "24^2 + 15^2 = y^2<BR>\n" );
document.write( "576 + 225 = y^2<BR>\n" );
document.write( "801 = y^2<BR>\n" );
document.write( "28.3 feet = y (ladder's length)\r<BR>\n" );
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