document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72608>Question 72608</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Geometry. If the sides of a square are decreased by 2cmm the area is decreased by 36cm^2. What were the dimensions of the original square?: \r<BR>\n" );
document.write( "\n" );
document.write( "I did not see how this was solved??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51904 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=51904\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the original length of the side of the square be represented by L. Since the area of a <BR>\n" );
document.write( "square equals the square of a side we can by letting A represent the original area write the<BR>\n" );
document.write( "equation:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+L%5E2 ALIGN=MIDDLE  ALT=\"A+=+L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now what happens when we decrease the length of the side by 2 cm? The new length of the side<BR>\n" );
document.write( "is the old length minus 2 cm or L - 2.  And we are told that the new area of the square is<BR>\n" );
document.write( "old area A minus 36 square cm or A - 36.  Now for the new square, let's write the area equation<BR>\n" );
document.write( "that says the Area = the square of a side:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+-+36+=+%28L-2%29%5E2 ALIGN=MIDDLE  ALT=\"A+-+36+=+%28L-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "but we said previously that A is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2 ALIGN=MIDDLE  ALT=\"L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2 ALIGN=MIDDLE  ALT=\"L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > for A into our<BR>\n" );
document.write( "equation we get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2+-+36+=+%28L-2%29%5E2 ALIGN=MIDDLE  ALT=\"L%5E2+-+36+=+%28L-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and by squaring the right side we get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2+-+36+=+L%5E2+-+4L+%2B+4 ALIGN=MIDDLE  ALT=\"L%5E2+-+36+=+L%5E2+-+4L+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Then you can subtract L^2 from both sides to reduce the equation to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-36+=+-4L+%2B+4 ALIGN=MIDDLE  ALT=\"-36+=+-4L+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Add 4L to both sides to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4L+-+36+=+4 ALIGN=MIDDLE  ALT=\"4L+-+36+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Then add 36 to both sides:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4L+=+40 ALIGN=MIDDLE  ALT=\"4L+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Finally, divide both sides by 4 to end up with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+10 ALIGN=MIDDLE  ALT=\"L+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the answer is in cm. So the <BR>\n" );
document.write( "dimensions of the original square (represented by L) were 10 cm on a side.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this untangles the problem for you and helps you to see how to deal with problems such <BR>\n" );
document.write( "as these. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );