document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=243737>Question 243737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a rectangle is 80 square feet. The length is 2 feet longer than the width. Find the measure of each. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #178542 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=178542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We know the area of a rectangle is width times the length.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+W+%2A+L ALIGN=MIDDLE  ALT=\"A+=+W+%2A+L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "We are told A = 80<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We also are told L is 2 feet longer than the width.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+W+%2B+2 ALIGN=MIDDLE  ALT=\"L+=+W+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+L+-+2 ALIGN=MIDDLE  ALT=\"W+=+L+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You pick.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substituting what we know:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+W+%2A+L ALIGN=MIDDLE  ALT=\"A+=+W+%2A+L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80+=+%28L-2%29+%2A+L ALIGN=MIDDLE  ALT=\"80+=+%28L-2%29+%2A+L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying through the right-hand:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80+=+L%5E2+-+2L ALIGN=MIDDLE  ALT=\"80+=+L%5E2+-+2L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equal things are equal, so we can rewrite:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2+-+2L+=+80 ALIGN=MIDDLE  ALT=\"L%5E2+-+2L+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subracting 80 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2+-+2L+-+80+=+0 ALIGN=MIDDLE  ALT=\"L%5E2+-+2L+-+80+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "We now consider whether it can be factored.  The factors of 80 are 2*40, 4*20, 5*18, 8*10...<BR>\n" );
document.write( "We have to have different signs to get them to multiply to -80.<BR>\n" );
document.write( "And we need them to be 2 apart to have the solve the L term.  8 & 10 is the way to go.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L-10%29%28L%2B8%29+=+0 ALIGN=MIDDLE  ALT=\"%28L-10%29%28L%2B8%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "So we have two candidate solutions:  L=10 and L=-8.<BR>\n" );
document.write( "Since we are talking about the area of a rectangle, a length of -8 is not reasonable.  So we'll test 10.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Looking back at the equations we established:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+L+-+2+=+10+-+2+=+8 ALIGN=MIDDLE  ALT=\"W+=+L+-+2+=+10+-+2+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "So we propose the L=10 and W=8.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Checking the Area, we test:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+L+%2A+W+=+10+%2A+8+=+80 ALIGN=MIDDLE  ALT=\"A+=+L+%2A+W+=+10+%2A+8+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "That checks. So we're done. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );