document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126609>Question 126609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the length of a rectangle is 7 feet more than width. if the length were decreased by 3 feet and the width were increased by 2 feet, the perimeter would be 32 feet. Find the length of the original rectangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92772 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=92772\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The length of the original rectangle is L, and the width is W.  We also know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=W%2B7 ALIGN=MIDDLE  ALT=\"L=W%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "If we decrease the length by 3 we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L-3 ALIGN=MIDDLE  ALT=\"L-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and if we increase the width by 2, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%2B2 ALIGN=MIDDLE  ALT=\"W%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The perimeter of a rectangle is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2L%2B2W ALIGN=MIDDLE  ALT=\"P=2L%2B2W\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but we only know the perimeter of the new rectangle, so we have to use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bn%5D=2%28L-3%29%2B2%28W%2B2%29=32 ALIGN=MIDDLE  ALT=\"P%5Bn%5D=2%28L-3%29%2B2%28W%2B2%29=32\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   But while we're at it, let's substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%2B7 ALIGN=MIDDLE  ALT=\"W%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > for L so that we have a single equation in a single unknown.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bn%5D=2%28%28W%2B7%29-3%29%2B2%28W%2B2%29=32 ALIGN=MIDDLE  ALT=\"P%5Bn%5D=2%28%28W%2B7%29-3%29%2B2%28W%2B2%29=32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now collect terms and solve:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%2B8%2B2W%2B4=32 ALIGN=MIDDLE  ALT=\"2W%2B8%2B2W%2B4=32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4W%2B12=32 ALIGN=MIDDLE  ALT=\"4W%2B12=32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4W=20 ALIGN=MIDDLE  ALT=\"4W=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=5 ALIGN=MIDDLE  ALT=\"W=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since W is 5, L must be 5 + 7 = 12.\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "If we decrese the length by 3, we get 9, and if we increase the width by 2 we get 7.  (2 * 9) + (2 * 7) = 18 + 14 = 32.  Answer checks. </SPAN>\n" );
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