document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92555>Question 92555</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Geomatry. If the sides of a square are decreased by 2cm, the area is decreased by 36cm^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #67375 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=67375\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x be the length of the side of the original square. Therefore, the area of the original<BR>\n" );
document.write( "square is x^2.<BR>\n" );
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document.write( "Now take 2 cm off each side of the original square. That means that the length of the side<BR>\n" );
document.write( "of the new square is x-2 cm. You square this to get the area of this new square. So the<BR>\n" );
document.write( "area of the new square is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2+=+x%5E2+-4x+%2B+4 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2+=+x%5E2+-4x+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The problem then says that the difference between the original area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the new <BR>\n" );
document.write( "area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+4x+%2B4%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+4x+%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 36 cm^2. Setting this up as an equation we have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+%28x%5E2+-+4x+%2B4%29+=+36 ALIGN=MIDDLE  ALT=\"x%5E2+-+%28x%5E2+-+4x+%2B4%29+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since the parentheses are preceded by a minus sign, you can remove the parentheses<BR>\n" );
document.write( "by changing the signs of the terms within the parentheses. This leads to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x%5E2+%2B+4x+-+4+=+36 ALIGN=MIDDLE  ALT=\"x%5E2+-+x%5E2+%2B+4x+-+4+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms cancel each other due to their difference in signs. So<BR>\n" );
document.write( "they drop from the equation which then becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+-+4+=+36 ALIGN=MIDDLE  ALT=\"4x+-+4+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the -4 on the left side by adding +4 to both sides. This reduces the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+=+40 ALIGN=MIDDLE  ALT=\"4x+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for x by dividing both sides by 4 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+40%2F4+=+10 ALIGN=MIDDLE  ALT=\"x+=+40%2F4+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the length of each side of the original square is 10 cm.<BR>\n" );
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document.write( "And the length of each side of the new square is 10 - 2 or 8 cm.<BR>\n" );
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document.write( "Check. The area of the original square is 10*10 = 100 cm^2. The area of the new square is<BR>\n" );
document.write( "8 * 8 = 64 cm^2. <BR>\n" );
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document.write( "The difference in their areas is 100 cm^2 - 36 cm^2 = 64 cm^2.<BR>\n" );
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document.write( "Hope that the answer you were looking for is in here somewhere. This will probably <BR>\n" );
document.write( "give you the process you can use to solve this problem. </SPAN>\n" );
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