document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103990>Question 103990</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Word problem: The side of a square has length S. The length of a rectangle is 4m more than the side of the square and the width of the rectangle is 2m less than the side of the square.  The perimeter of the rectangle is 24m less than twice the perimeter of the square.  Find the dimension of each figure.  \r<BR>\n" );
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document.write( "Please help...no idea where to begin.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75660 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=75660\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let L=length of the rectangle, w=width of the rectangle, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bs%5D ALIGN=MIDDLE  ALT=\"P%5Bs%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= perimeter of the square, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Br%5D ALIGN=MIDDLE  ALT=\"P%5Br%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= perimeter of the rectangle\r<BR>\n" );
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document.write( "Let's start with what we know and what we are given\r<BR>\n" );
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document.write( "This is what we are given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=4%2BS ALIGN=MIDDLE  ALT=\"L=4%2BS\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"The length of a rectangle is 4m more than the side of the square\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=S-2 ALIGN=MIDDLE  ALT=\"W=S-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"the width of the rectangle is 2m less than the side of the square\r<BR>\n" );
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document.write( "And this is what we know :\r<BR>\n" );
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document.write( "Perimeter of the square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bs%5D=4S ALIGN=MIDDLE  ALT=\"P%5Bs%5D=4S\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( " Perimeter of the rectangle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Br%5D=2L%2B2W ALIGN=MIDDLE  ALT=\"P%5Br%5D=2L%2B2W\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remember, the problem says: \"The perimeter of the rectangle is 24m less than twice the perimeter of the square\". So this means the perimeter of the rectangle is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Br%5D=2P%5Bs%5D-24 ALIGN=MIDDLE  ALT=\"P%5Br%5D=2P%5Bs%5D-24\"   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=P%5Bs%5D=4S ALIGN=MIDDLE  ALT=\"P%5Bs%5D=4S\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can substitute that into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Br%5D=2P%5Bs%5D-24 ALIGN=MIDDLE  ALT=\"P%5Br%5D=2P%5Bs%5D-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=P%5Br%5D=2%284S%29-24 ALIGN=MIDDLE  ALT=\"P%5Br%5D=2%284S%29-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bs%5D=4S ALIGN=MIDDLE  ALT=\"P%5Bs%5D=4S\"   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=P%5Br%5D=8S-24 ALIGN=MIDDLE  ALT=\"P%5Br%5D=8S-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply \r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Br%5D=8S-24 ALIGN=MIDDLE  ALT=\"P%5Br%5D=8S-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Br%5D=2L%2B2W ALIGN=MIDDLE  ALT=\"P%5Br%5D=2L%2B2W\"   DISABLED_style= \"max-width:90%; height:auto;\" >, set them 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=8S-24=2L%2B2W ALIGN=MIDDLE  ALT=\"8S-24=2L%2B2W\"   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=8S-24=2%284%2BS%29%2B2%28S-2%29 ALIGN=MIDDLE  ALT=\"8S-24=2%284%2BS%29%2B2%28S-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=4%2BS ALIGN=MIDDLE  ALT=\"L=4%2BS\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=S-2 ALIGN=MIDDLE  ALT=\"W=S-2\"   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=8S-24=8%2B2S%2B2S-4 ALIGN=MIDDLE  ALT=\"8S-24=8%2B2S%2B2S-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8S-24=4S%2B4 ALIGN=MIDDLE  ALT=\"8S-24=4S%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8S=4S%2B4%2B24 ALIGN=MIDDLE  ALT=\"8S=4S%2B4%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 24 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8S-4S=4%2B24 ALIGN=MIDDLE  ALT=\"8S-4S=4%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 4S from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4S=4%2B24 ALIGN=MIDDLE  ALT=\"4S=4%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4S=28 ALIGN=MIDDLE  ALT=\"4S=28\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%2828%29%2F%284%29 ALIGN=MIDDLE  ALT=\"S=%2828%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4 to isolate S\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=7 ALIGN=MIDDLE  ALT=\"S=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=7 ALIGN=MIDDLE  ALT=\"S=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the side length of the square is 7m. This means the length of the rectangle is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=4%2BS=4%2B7=11 ALIGN=MIDDLE  ALT=\"L=4%2BS=4%2B7=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the length is 11m\r<BR>\n" );
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document.write( "This also means the width of the rectangle is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=S-2=7-2=5 ALIGN=MIDDLE  ALT=\"W=S-2=7-2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the width is 5m\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "First find the perimeter of the square:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=4S=4%287%29=28 ALIGN=MIDDLE  ALT=\"P=4S=4%287%29=28\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now multiply 28 by 2 and subtract 24 to get...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28%2A2-24=32 ALIGN=MIDDLE  ALT=\"28%2A2-24=32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now find the perimeter of the rectangle\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2L%2B2W=2%2811%29%2B2%285%29=22%2B10=32 ALIGN=MIDDLE  ALT=\"P=2L%2B2W=2%2811%29%2B2%285%29=22%2B10=32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the perimeter of the rectangle is 24 less than twice the perimeter of the square, our answer is verified </SPAN>\n" );
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