document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145407>Question 145407</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the distance of its top to the ground is 4 feet less than the length of 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 #106086 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=106086\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the distance of its top to the ground is 4 feet less than the length of the ladder.<BR>\n" );
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document.write( "Using the formula a^2 + b^2 = c^2<BR>\n" );
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document.write( "Let x = length of the ladder (c)<BR>\n" );
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document.write( "\"The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder.\" Therefore:<BR>\n" );
document.write( "(x-3) = a<BR>\n" );
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document.write( "\"the distance of its top to the ground is 4 feet less than the length of the ladder.\" therefore:<BR>\n" );
document.write( "(x-4) = b<BR>\n" );
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document.write( "Using the formula we have:<BR>\n" );
document.write( "(x-3)^2 + (x-4)^2 = x^2<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "(x^2 - 6x + 9) + (x^2 - 8x + 16) = x^2<BR>\n" );
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document.write( "Combine like terms on the left<BR>\n" );
document.write( "x^2 + x^2 - x^2 - 6x - 8x + 9 + 16 = 0<BR>\n" );
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document.write( "x^2 - 14x + 25 = 0<BR>\n" );
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document.write( "Solve for x using the quadratic formula; <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " a=1; b=-14; c=25<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-14%29+%2B-+sqrt%28-14%5E2+-+4+%2A+1+%2A+25+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-14%29+%2B-+sqrt%28-14%5E2+-+4+%2A+1+%2A+25+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2814+%2B-+sqrt%28196+-+100+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2814+%2B-+sqrt%28196+-+100+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "you can do the math here, the reasonable solution is x = 11.9' length of ladder <BR>\n" );
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document.write( "Check solution<BR>\n" );
document.write( "8.9^2 + 7.9^2 = 141.6 which is 11.9 squared\r<BR>\n" );
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document.write( " </SPAN>\n" );
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