document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166487>Question 166487</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a rectangle is 46m. If the width were doubled and the length were increased by 6 m, the perimeter would be 70 m. What are the length and width of the rectangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122688 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=122688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let L = length of original rectangle.<BR>\n" );
document.write( "let W = width of original rectangle.<BR>\n" );
document.write( "formula for perimeter of the original rectangle:<BR>\n" );
document.write( "2*L + 2*W = 46m (equation 1) *************************************<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let L+6 = length of modified rectangle.<BR>\n" );
document.write( "let 2*W = width of modified rectangle.<BR>\n" );
document.write( "formula for perimeter of modified rectangle:<BR>\n" );
document.write( "2 * (L+6) + 2 * (2*W) = 70m (original equation 2)<BR>\n" );
document.write( "expand this out more:<BR>\n" );
document.write( "(2*L) + (2*6) + (2*2*W) = 70m<BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "2*L + 12 + 4*W = 70m <BR>\n" );
document.write( "subtract 12 from both sides:<BR>\n" );
document.write( "2*L + 4*W = 58 (equation 2) **************************************<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you have 2 equations that you want to solve simultaneously so that the same solution is applicable to both.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "2*L + 2*W = 46 (equation 1)<BR>\n" );
document.write( "2*L + 4*W = 58 (equation 2)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since they have a common term that can be eliminated (2*L), just subtract equation 1 from equation 2:<BR>\n" );
document.write( "2*W = 12<BR>\n" );
document.write( "W = 6<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you have W = 6.<BR>\n" );
document.write( "substitute in equation 1:<BR>\n" );
document.write( "2*L + 2*6 = 46<BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "2*L + 12 = 46<BR>\n" );
document.write( "subtract 12 from both sides:<BR>\n" );
document.write( "2*L = 34<BR>\n" );
document.write( "divide both sides by 2:<BR>\n" );
document.write( "L = 17<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "W = 6<BR>\n" );
document.write( "L = 17<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substitute in original equation 2:<BR>\n" );
document.write( "2 * (17+6) + 2*(2*6) = 70<BR>\n" );
document.write( "perform indicated operations:<BR>\n" );
document.write( "2*23 + 2*12 = 70<BR>\n" );
document.write( "46 + 24 = 70<BR>\n" );
document.write( "70 = 70<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer is good:<BR>\n" );
document.write( "length of the original rectangle is 17 meters and width of the original rectangle is 6 meters.<BR>\n" );
document.write( "-----\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );