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 #64729 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=64729\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We basically have this triangle set up:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-0.5%2C3%2C-0.5%2C3%2C%0D%0A%0D%0Aline%280%2C0%2C0%2C3%29%2C%0D%0Aline%280%2C3%2C2%2C0%29%2C%0D%0Aline%282%2C0%2C0%2C0%29%2C%0D%0Alocate%28-0.2%2C1.5%2Ca%29%2C%0D%0Alocate%281%2C-0.2%2C15%29%2C%0D%0Alocate%281%2C2%2Cc%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B15%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2B15%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Here is the original Pythagorean equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-0.5%2C5%2C-0.5%2C5%2C%0D%0A%0D%0Ablue%28line%280%2C0%2C0%2C3%29%29%2C%0D%0Ablue%28line%280%2C3%2C2%2C0%29%29%2C%0D%0Ablue%28line%282%2C0%2C0%2C0%29%29%2C%0D%0A%0D%0Agreen%28line%280%2C0%2C0%2C1%29%29%2C%0D%0Agreen%28line%280%2C1%2C4%2C0%29%29%2C%0D%0Agreen%28line%284%2C0%2C0%2C0%29%29%2C%0D%0Alocate%28-0.2%2C1.5%2Ca%29%2C%0D%0Alocate%28-0.2%2C0.5%2Ca-13%29%2C%0D%0Alocate%281%2C-0.2%2C15%29%2C%0D%0Alocate%282.2%2C-0.2%2C15%2B9%29%2C%0D%0Alocate%281%2C2%2Cc%29%2C%0D%0Alocate%282.5%2C0.6%2Cc%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Here is the original position of the ladder (blue) and the shifted ladder (green)\r<BR>\n" );
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document.write( "Notice that we subtract 13 from a to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-13 ALIGN=MIDDLE  ALT=\"a-13\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So our new \"a\" is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-13 ALIGN=MIDDLE  ALT=\"a-13\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Also, we add 9 to our base to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2B9 ALIGN=MIDDLE  ALT=\"15%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So our new \"b\" is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2B9=24 ALIGN=MIDDLE  ALT=\"15%2B9=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-13%29%5E2%2B24%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"%28a-13%29%5E2%2B24%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > So if we shift the ladder, we get this equation. \r<BR>\n" );
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document.write( "Notice how the 2 equations are equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2 ALIGN=MIDDLE  ALT=\"c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so that means we can set the two equations equal to each other\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-13%29%5E2%2B576=a%5E2%2B225 ALIGN=MIDDLE  ALT=\"%28a-13%29%5E2%2B576=a%5E2%2B225\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%5E2 ALIGN=MIDDLE  ALT=\"24%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%5E2 ALIGN=MIDDLE  ALT=\"15%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-26a%2B169%2B576=a%5E2%2B225 ALIGN=MIDDLE  ALT=\"a%5E2-26a%2B169%2B576=a%5E2%2B225\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-13%29%5E2 ALIGN=MIDDLE  ALT=\"%28a-13%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-26a%2B745=a%5E2-520 ALIGN=MIDDLE  ALT=\"a%5E2-26a%2B745=a%5E2-520\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-26a%2B745=-520 ALIGN=MIDDLE  ALT=\"-26a%2B745=-520\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-26a=-520 ALIGN=MIDDLE  ALT=\"-26a=-520\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 745 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=20 ALIGN=MIDDLE  ALT=\"a=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -26\r<BR>\n" );
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document.write( "So the original height of the ladder is 20 feet, and it drops to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20-13=7 ALIGN=MIDDLE  ALT=\"20-13=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet. Lets check our answer:\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5E2%2B15%5E2=400%2B225=625 ALIGN=MIDDLE  ALT=\"20%5E2%2B15%5E2=400%2B225=625\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5E2%2B24%5E2=49%2B576=625 ALIGN=MIDDLE  ALT=\"7%5E2%2B24%5E2=49%2B576=625\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the 2 equations are equal, this means that we get the same hypotenuse. So the ladder is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28625%29=25 ALIGN=MIDDLE  ALT=\"sqrt%28625%29=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet long. This also verifies our answer. </SPAN>\n" );
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