document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=844240>Question 844240</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the perimeter of a rectangle is 26 centimeters. the area of the rectangle remains the same if the length is decreased by 3 centimeters and the width is increased by 2 centimeters. what is the dimensions of the original rectangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #508635 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=508635\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P = perimeter<BR>\n" );
document.write( "L = length<BR>\n" );
document.write( "W = width<BR>\n" );
document.write( "formula for P is P = 2L + 2W<BR>\n" );
document.write( "A = area<BR>\n" );
document.write( "formula for A is A = LW\r<BR>\n" );
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document.write( "you are given that:<BR>\n" );
document.write( "P = 26<BR>\n" );
document.write( "This means that:<BR>\n" );
document.write( "2L + 2W = 26\r<BR>\n" );
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document.write( "you know that LW = A, but you don't know what A is.<BR>\n" );
document.write( "you are also given that (L-3)*(W+2) = A.<BR>\n" );
document.write( "Since they are both equal to A, you can make LW equal to (L-3)*(W+2)<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "LW = (L-3) * (W+2)<BR>\n" );
document.write( "simplify this equation to get:<BR>\n" );
document.write( "LW = LW + 2L - 3W - 6<BR>\n" );
document.write( "subtract LW from both sides of this equation to get:<BR>\n" );
document.write( "0 = 2L - 3W - 6<BR>\n" );
document.write( "Add 3W to both sides of this equation to get:<BR>\n" );
document.write( "3W = 2L - 6<BR>\n" );
document.write( "Divide both sides of this equation by 3 to get:<BR>\n" );
document.write( "W = 2/3 * L - 2\r<BR>\n" );
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document.write( "you know that 2L + 2W = 26<BR>\n" );
document.write( "replace W with 2/3 * L - 2 in that equation to get:<BR>\n" );
document.write( "2L + 2 * (2/3 * L - 2) = 26<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "2L + 4/3 * L - 4 = 26<BR>\n" );
document.write( "add 4 to both sides of this equation to get:<BR>\n" );
document.write( "2L + 4/3 * L = 30<BR>\n" );
document.write( "Multiply both sides of this equation by 3 to get:<BR>\n" );
document.write( "6L + 4L = 90<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "10L = 90<BR>\n" );
document.write( "divide both sides of this equation by 10 to get:<BR>\n" );
document.write( "L = 9\r<BR>\n" );
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document.write( "go back to your original equation for P to get:<BR>\n" );
document.write( "2L + 2W = 26<BR>\n" );
document.write( "replace L with 9 to get:<BR>\n" );
document.write( "18 + 2W = 26<BR>\n" );
document.write( "subtract 18 from both sides of this equation to get:<BR>\n" );
document.write( "2W = 8<BR>\n" );
document.write( "divide both sides of this equation by 2 to get:<BR>\n" );
document.write( "W = 4\r<BR>\n" );
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document.write( "your solution is:<BR>\n" );
document.write( "L = 9<BR>\n" );
document.write( "W = 4\r<BR>\n" );
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document.write( "Your perimeters becomes 2 * 9 + 2 * 4 = 18 + 8 = 26<BR>\n" );
document.write( "The area is 9 * 4 = 36<BR>\n" );
document.write( "subtract 3 from 9 and add 2 to 4 and you get:<BR>\n" );
document.write( "The area is 6 * 6 = 36\r<BR>\n" );
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document.write( "The area remained the same when you subtracted 3 from the length and added 2 to the width.<BR>\n" );
document.write( "The solution is good.<BR>\n" );
document.write( "L = 9<BR>\n" );
document.write( "W = 4\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );