document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=39896>Question 39896</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072549017/algebrahomeworkh>Beginning Algebra </A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm^2. What were the dimensions of the original square?<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #25335 by </B><A HREF=/tutors/aboutme.mpl?userid=Fermat><B>Fermat(136)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fermat><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=Fermat><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=25335\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If what you have is a square, then both the sides have the same size.<BR>\n" );
document.write( "Let the size of the square be x.<BR>\n" );
document.write( "Then the area of the square is,<BR>\n" );
document.write( "A = x * x = x^2<BR>\n" );
document.write( "A = x^2<BR>\n" );
document.write( "=======<BR>\n" );
document.write( "The new sides of the square are now x-2.<BR>\n" );
document.write( "The new area of the square is therefore,<BR>\n" );
document.write( "A2 = (x-2) * (x-2) = (x-2)^2<BR>\n" );
document.write( "A2 = (x-2)^2<BR>\n" );
document.write( "============<BR>\n" );
document.write( "We are told that the new area, A2 is 36 cm^2 less than the original square. So we can write,<BR>\n" );
document.write( "A2 = A - 36<BR>\n" );
document.write( "Substituting for A = x^2 and A2 = (x-2)^2, we get<BR>\n" );
document.write( "(x-2)^2 = x^2 - 36<BR>\n" );
document.write( "now exand the brackets on the lhs,<BR>\n" );
document.write( "x^2 - 4x + 4 = x^2 - 36<BR>\n" );
document.write( "subtract x^2 from both sides,<BR>\n" );
document.write( "-4x + 4 = -36<BR>\n" );
document.write( "change the signs of all the terms,<BR>\n" );
document.write( "4x - 4 = 36<BR>\n" );
document.write( "add 4 to both sides,<BR>\n" );
document.write( "4x = 40<BR>\n" );
document.write( "divide both sides by 4,<BR>\n" );
document.write( "x = 10 cm<BR>\n" );
document.write( "========= </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );