document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=89044>Question 89044</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ladder leans against a house with it's base 15 feet from the house. When the ladder is pulled 9 feet further away from the house the upper end slides down 13 feet. How long is the ladder?<BR>\n" );
document.write( "I understand how to figure Pythagoreans theorem with one variable, but how do you do it with two variables? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64727 by </B><A HREF=/tutors/aboutme.mpl?userid=malakumar_kos@yahoo.com><B>malakumar_kos@yahoo.com(315)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=malakumar_kos@yahoo.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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=64727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "    A ladder leans against a house with it's base 15 feet from the house. When the ladder is pulled 9 feet further away from the house the upper end slides down 13 feet. How long is the ladder?<BR>\n" );
document.write( "I understand how to figure Pythagoreans theorem with one variable, but how do you do it with two variables?\r<BR>\n" );
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document.write( "      Let ABC  be a right angled triangle such that angle A = 90 degrees\r<BR>\n" );
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document.write( "     BC will be the hypotenuse, AB willbe the distance at which the foot of the ladder stands from the house, AC is the height at which the top of the ladder <BR>\n" );
document.write( " meets the building.Let the height of the building be = x  ft <BR>\n" );
document.write( "    applying pythagorous theorem  we get BC^2 = AB^2+AC^2  (AC=15  ft)\r<BR>\n" );
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document.write( "           Therefore BC^2 = x^2+15^2...........eq'n (1)\r<BR>\n" );
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document.write( "     When the ladder is pulled 9 ft away from the house  the upper end slides \r<BR>\n" );
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document.write( "     13 ftdown. The new triangle formed will be ADE  such that DE is the \r<BR>\n" );
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document.write( "     hypotenuse  , AD = x-13 , and AE = 15+9 = 24  ft\r<BR>\n" );
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document.write( "     In both the triangles the hypotenuse represents the length of the ladder   which is a constant for a given ladder.\r<BR>\n" );
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document.write( "     applying Pythagorous theorem  for triangle ADE we get  DE^2 = AD^2+AE^2\r<BR>\n" );
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document.write( "                               or DE^2 = (x-13)^2+(24)^2..........eq'n(2)\r<BR>\n" );
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document.write( "         From eq'n(1) &eq'n(2)  (x-13)^2+(24)^2 = x^2+15^2     (BC = DE)\r<BR>\n" );
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document.write( "                                 x^2+169-26x+576 = x^2+225\r<BR>\n" );
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document.write( "                                      169+576-225 = 26x\r<BR>\n" );
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document.write( "                                       745-225 = 26x\r<BR>\n" );
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document.write( "                                        520    = 26x\r<BR>\n" );
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document.write( "                                           x  = 520/26 = 20  ft<BR>\n" );
document.write( "         To find thelength of the ladder  substitite the value of x in eq'n (1)\r<BR>\n" );
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document.write( "         Therefore  BC^2 = x^2+15^2<BR>\n" );
document.write( "                         = 20^2+15^2<BR>\n" );
document.write( "                         = 400+225<BR>\n" );
document.write( "                         = 625\r<BR>\n" );
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document.write( "                   BC = sq rt of 625 = 25  ft <BR>\n" );
document.write( "      Therefore the length of the ladder  = 25 ft\r<BR>\n" );
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document.write( "       \r<BR>\n" );
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document.write( "                                                       </SPAN>\n" );
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