document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161047>Question 161047</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9781567655858/algebrahomeworkh>Amsco's Integrated Algebra 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Hi I really need help on my math homework. Here is the question: The length of a rectangle exceeds its width by 4 feet. If the width is doubled and the length is decreased by 2 feet, a new rectangle is formed whose perimeter is 8 feet more than the perimeter of the original rectangle. Find the dimensions of the original rectangle.<BR>\n" );
document.write( "My teacher says that we have to do \"let\" statements first. Her are mine:<BR>\n" );
document.write( "Let x= the width of the rectangle<BR>\n" );
document.write( "Let x + 4= the length of the rectangle<BR>\n" );
document.write( "I am not sure if these let statements are right, and if they are i  am not sure how to set up the equation. Thanks for help  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118659 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=118659\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "YOU ARE ABSOLUTELY RIGHT IN YOUR APPROACH SO FAR:<BR>\n" );
document.write( "Now given what you have done, we know that the perimeter of a rectangle is 2w+2l<BR>\n" );
document.write( "So, the perimeter of the original rectangle is:<BR>\n" );
document.write( "2x+2(x+4) <BR>\n" );
document.write( "Now if we double the width, we get: 2x<BR>\n" );
document.write( "And if we decrease the length by 2, we get: x+4-2=x+2<BR>\n" );
document.write( "Now the new perimeter would be 2*2x+2(x+2)=4x+2(x+2) and we are told that this new perimeter is 8 feet more than the perimeter of the original rectangle, so our equation to solve is:<BR>\n" );
document.write( "Original perimeter +8 =new perimeter, or<BR>\n" );
document.write( "2x+2(x+4)+8=4x+2(x+2)  get rid of parens (distributive law)<BR>\n" );
document.write( "2x+2x+8+8=4x+2x+4  collect like terms<BR>\n" );
document.write( "4x+16=6x+4 subtract 4x and also 4 from each side<BR>\n" );
document.write( "4x-4x+16-4=6x-4x+4-4  collect like terms again<BR>\n" );
document.write( "12=2x divide each side by 2<BR>\n" );
document.write( "x=6 ft--------------------------width of the original rectangle<BR>\n" );
document.write( "x+4=6+4=10 ft----------------------length of the original rectangle\r<BR>\n" );
document.write( "\n" );
document.write( "CK<BR>\n" );
document.write( "perimeter of original rectangle=2*6+2*10=32 ft<BR>\n" );
document.write( "perimeter of new rectangle=2*12+2*8=40 ft<BR>\n" );
document.write( "40-32=8<BR>\n" );
document.write( "8=8\r<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps----ptaylor<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );