document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171289>Question 171289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need your help on the following word problem:<BR>\n" );
document.write( "A rectangle is 15cm wide and 18cm long. If both dimensions are decreased by the same amount, the area of the new rectangle is 116cm squared less than the area of the original. Find the dimensions of the new rectangle.<BR>\n" );
document.write( "Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126452 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=126452\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the original dimensions are 15 by 18 and they are both reduced by the same amount, then the new dimensions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+3 ALIGN=MIDDLE  ALT=\"x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The original area was 15 times 18 or 270 square centimeters.  116 square centimeters less than 270 is 154 square centimeters which is the area of the new rectangle.\r<BR>\n" );
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document.write( "So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B3%29=154 ALIGN=MIDDLE  ALT=\"x%28x%2B3%29=154\"   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=x%5E2%2B3x-154=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x-154=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%2A14=-154 ALIGN=MIDDLE  ALT=\"-11%2A14=-154\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%2B14=3 ALIGN=MIDDLE  ALT=\"-11%2B14=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the quadratic factors to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-11%29%28x%2B14%29=0 ALIGN=MIDDLE  ALT=\"%28x-11%29%28x%2B14%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11 ALIGN=MIDDLE  ALT=\"x=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-14 ALIGN=MIDDLE  ALT=\"x=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-14 is absurd because you can't have a negative dimension, so exclude this root as extraneous.  That means that the new width of the rectangle is 11, and the new length is 3 more than that or 14.\r<BR>\n" );
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document.write( "Check:  11 * 14 = 154, 154 + 116 = 270, 15 - 4 = 11, and 18 - 4 = 14.  So all the original problem parameters are satisfied.  Answer checks. </SPAN>\n" );
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