document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114394>Question 114394</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the sides of a square are decreased by 2cm, the area is decreased by 36 cm squared. What were the dimensions of the original square? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83279 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=83279\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with defining a variable to represent the length of a side of the original square, let's call it x.\r<BR>\n" );
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document.write( "So the area of the original square would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D=x%5E2 ALIGN=MIDDLE  ALT=\"A%5Bo%5D=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The new square is 2 cm shorter on each side, so one of the sides must measure <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;\" >, and the area of the new square must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bn%5D=%28x-2%29%5E2 ALIGN=MIDDLE  ALT=\"A%5Bn%5D=%28x-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "But we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D=A%5Bn%5D%2B36cm%5E2 ALIGN=MIDDLE  ALT=\"A%5Bo%5D=A%5Bn%5D%2B36cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Substituting:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=%28x-2%29%5E2%2B36 ALIGN=MIDDLE  ALT=\"x%5E2=%28x-2%29%5E2%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now, expand the binomial, collect terms, and put the equation in standard form.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=x%5E2-4x%2B4%2B36 ALIGN=MIDDLE  ALT=\"x%5E2=x%5E2-4x%2B4%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x%5E2=x%5E2-x%5E2-4x%2B40 ALIGN=MIDDLE  ALT=\"x%5E2-x%5E2=x%5E2-x%5E2-4x%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%2B40=0 ALIGN=MIDDLE  ALT=\"-4x%2B40=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the original square was 10 cm on a side.\r<BR>\n" );
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document.write( "Let's check the answer.\r<BR>\n" );
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document.write( "Original area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E2=100 ALIGN=MIDDLE  ALT=\"10%5E2=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "New area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E2=64 ALIGN=MIDDLE  ALT=\"8%5E2=64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100-64=36 ALIGN=MIDDLE  ALT=\"100-64=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Check. </SPAN>\n" );
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