document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84570>Question 84570</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0073048313/algebrahomeworkh>algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> If the sides of a square are decreased by 2cm, the area is decreased by 36cm^2, what were the dimensions of the original square?\r<BR>\n" );
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document.write( "I am very much stuck, how do I do this?<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 #60909 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=60909\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x represent the length of the side of a square.<BR>\n" );
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document.write( "Therefore, the area (A) of this square is given by the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B1%5D+=+x%5E2 ALIGN=MIDDLE  ALT=\"A%5B1%5D+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Shorten the length of the side of the square by 2 cm.  This means that the length of the side<BR>\n" );
document.write( "is now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+2 ALIGN=MIDDLE  ALT=\"x+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm.<BR>\n" );
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document.write( "The area of this new square is given by the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B2%5D+=+%28x+-+2%29%5E2+=+x%5E2+-4x+%2B+4 ALIGN=MIDDLE  ALT=\"A%5B2%5D+=+%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 difference of this area and the area of the original square is 36 cm^2. In equation <BR>\n" );
document.write( "form this becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B1%5D+-+A%5B2%5D+=+x%5E2+-+%28x%5E2+-+4x+%2B+4%29+=+x%5E2+-+x%5E2+%2B+4x+-+4+=+4x+-+4+=+36 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "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+-+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:<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 which is the multiplier of x.  This division<BR>\n" );
document.write( "results in:<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( "Since x was the side of the original square, we can now say that the side of the original<BR>\n" );
document.write( "square was 10 cm in length.<BR>\n" );
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document.write( "Check. The area of the original square would be 10 times 10 or 100 square cm. Shortening<BR>\n" );
document.write( "the sides by 2 cm would make the sides of the new square 8 cm in length.  The area of<BR>\n" );
document.write( "the new square would be 8 times 8 or 64 square cm. The difference between the 100 square<BR>\n" );
document.write( "cm area and the 64 square cm area is 36 square cm, just as the problem asked for it to be.<BR>\n" );
document.write( "This indicates that the answer of 10 cm as the length of a side of the original square is<BR>\n" );
document.write( "correct.<BR>\n" );
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document.write( "Hope this explanation helps you to work your way through the problem </SPAN>\n" );
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