document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202617>Question 202617</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle is half as wide as it is long. If both the length and width are decreased by 2 cm, the area decreases by 68 cm(squared) . Find the length 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 #152829 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=152829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the original length = L and the original width = W, so that the original area:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+L%2AW ALIGN=MIDDLE  ALT=\"A+=+L%2AW\"   DISABLED_style= \"max-width:90%; height:auto;\" > but the problem says that the \"...rectangle is half as wide as it is long.\", so this can be expressed as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%281%2F2%29L ALIGN=MIDDLE  ALT=\"W+=+%281%2F2%29L\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute this into the first equation and you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%281%2F2%29L%5E2 ALIGN=MIDDLE  ALT=\"A+=+%281%2F2%29L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, if we subtract 2 cm from the length (L-2) and 2 cm from the width (W-2) the area is decreased by 68 sq.cm. (A-68). Lets find the new area:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A-68+=+%28L-2%29%28W-2%29 ALIGN=MIDDLE  ALT=\"A-68+=+%28L-2%29%28W-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > but substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%281%2F2%29L ALIGN=MIDDLE  ALT=\"W+=+%281%2F2%29L\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%281%2F2%29L%5E2 ALIGN=MIDDLE  ALT=\"A+=+%281%2F2%29L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29L%5E2-68+=+%28L-2%29%28%281%2F2%29L-2%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29L%5E2-68+=+%28L-2%29%28%281%2F2%29L-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplifying:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29L%5E2-68+=+%281%2F2%29L%5E2-3L%2B4 ALIGN=MIDDLE  ALT=\"%281%2F2%29L%5E2-68+=+%281%2F2%29L%5E2-3L%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2L%5E2 ALIGN=MIDDLE  ALT=\"1%2F2L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-68+=+-3L%2B4 ALIGN=MIDDLE  ALT=\"-68+=+-3L%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 4 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-72+=+-3L ALIGN=MIDDLE  ALT=\"-72+=+-3L\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+24 ALIGN=MIDDLE  ALT=\"L+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%281%2F2%29L ALIGN=MIDDLE  ALT=\"W+=+%281%2F2%29L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+12 ALIGN=MIDDLE  ALT=\"W+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The original length of the rectangle is 24 cm.<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "Original area:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D+=+L%2AW ALIGN=MIDDLE  ALT=\"A%5Bo%5D+=+L%2AW\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute L=24 and W=12<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D+=+24%2A12 ALIGN=MIDDLE  ALT=\"A%5Bo%5D+=+24%2A12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D+=+288 ALIGN=MIDDLE  ALT=\"A%5Bo%5D+=+288\"   DISABLED_style= \"max-width:90%; height:auto;\" >sq.cm.<BR>\n" );
document.write( "Now the new area is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bn%5D+=+%28L-2%29%28W-2%29 ALIGN=MIDDLE  ALT=\"A%5Bn%5D+=+%28L-2%29%28W-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute L=24 and W=12<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bn%5D+=+%2824-2%29%2812-2%29 ALIGN=MIDDLE  ALT=\"A%5Bn%5D+=+%2824-2%29%2812-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bn%5D+=+%2822%29%2810%29 ALIGN=MIDDLE  ALT=\"A%5Bn%5D+=+%2822%29%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bn%5D+=+220 ALIGN=MIDDLE  ALT=\"A%5Bn%5D+=+220\"   DISABLED_style= \"max-width:90%; height:auto;\" >sq.cm.<BR>\n" );
document.write( "The difference is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bn%5D-A%5Bo%5D+=+288-220 ALIGN=MIDDLE  ALT=\"A%5Bn%5D-A%5Bo%5D+=+288-220\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=168 ALIGN=MIDDLE  ALT=\"168\"   DISABLED_style= \"max-width:90%; height:auto;\" >sq.cm. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );