document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169630>Question 169630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a rectangle is 15m^2 + 11m - 12. Find the length if the width is 5m-3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125053 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=125053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> area of a rectangle equals length * width.<BR>\n" );
document.write( "let A = area<BR>\n" );
document.write( "let L = length<BR>\n" );
document.write( "let W = width<BR>\n" );
document.write( "A = L*W<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you are given the area and the width.<BR>\n" );
document.write( "you want to find the length<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "A = L*W<BR>\n" );
document.write( "divide both sides of equation by W:<BR>\n" );
document.write( "A/W = L<BR>\n" );
document.write( "which is the same as:<BR>\n" );
document.write( "L = A/W<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "A = 15m^2 + 11m - 12<BR>\n" );
document.write( "W = 5m-3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substitute for A and W:<BR>\n" );
document.write( "L = (15m^2 + 11m - 12) / (5m-3)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this is a straight long division problem:<BR>\n" );
document.write( "first you figure how many times 5m will divide into 15m^2.<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "3m ********* this is the first part of your answer.<BR>\n" );
document.write( "then you multiply (5m-3) * 3m<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "(15m^2 - 9m)<BR>\n" );
document.write( "then you subtract (15m^2 - 9m) from (15m^2 + 11m - 12)<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "(15m^2 + 11m - 12) - (15m^2 - 9m) =<BR>\n" );
document.write( "15m^2 + 11m - 12 - 15m^2 + 9m =<BR>\n" );
document.write( "(20m - 12)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "next you figure out how many times 5m goes into 20m.<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "4 ********* this is the second part of your answer<BR>\n" );
document.write( "then you multiply (5m-3) * 4<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "(20m - 12)<BR>\n" );
document.write( "then you subtract (20m-12) from (20m - 12)<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "20m - 12 - (20m - 12) = <BR>\n" );
document.write( "20m - 12 - 20m + 12 =  <BR>\n" );
document.write( "0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your answer for (15m^2 + 11m - 12) / (5m-3) is (3m + 4)<BR>\n" );
document.write( "(3m+4) is the length.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to prove your answer is correct, go back to the original equation of:<BR>\n" );
document.write( "A = L*W<BR>\n" );
document.write( "substitute for A, L, and W:<BR>\n" );
document.write( "15m^2 + 11m - 12 = (3m+4)*(5m-3)<BR>\n" );
document.write( "(3m+4)*(5m-3) = 15m^2 - 9m + 20m - 12 =<BR>\n" );
document.write( "15m^2 + 11m - 12.<BR>\n" );
document.write( "this is the same as the area you started with so the equation is true proving that the value of (3m+4) for the length is good.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your answer is:<BR>\n" );
document.write( "length = (3m+4)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );