document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102565>Question 1102565</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the length of a rectangle is 4 centimeters more than the width. If both the width and the length were tripled, the area would be 108 square centimeters. Find the dimensions of the orginal rectangle<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717310 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=717310\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "When the length and width are both tripled (multiplied by 3), the area is increased by a factor of 3*3=9.  So the original area was 108/9=12.<br><BR>\n" );
document.write( "Inspection shows that two numbers that differ by 4 and have a product of 12 are 2 and 6; those are the dimensions of the original rectangle.<br><BR>\n" );
document.write( "If you need the formal algebra, it might look like this....<br><BR>\n" );
document.write( "let x = original width<BR>\n" );
document.write( "then x+4=original length<BR>\n" );
document.write( "3x = new width<BR>\n" );
document.write( "3(x+4) = 3x+12 = new length<br><BR>\n" );
document.write( "The new area (length times width) is 108:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%29%283x%2B12%29+=+108 ALIGN=MIDDLE  ALT=\"%283x%29%283x%2B12%29+=+108\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2%2B36x+=+108 ALIGN=MIDDLE  ALT=\"9x%5E2%2B36x+=+108\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2%2B36x-108+=+0 ALIGN=MIDDLE  ALT=\"9x%5E2%2B36x-108+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x-12+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x-12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29%28x-2%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B6%29%28x-2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = -6 or x = 2;<BR>\n" );
document.write( "reject the negative solution since it is the width<br<<BR>\n" );
document.write( "The original width was x=2; the original length was x+4=6.<br><BR>\n" );
document.write( "Learning how to solve the problem using formal algebra is good training, for when the problems get too complicated to solve informally by logical reasoning.<br><BR>\n" );
document.write( "But you should also be able to use your powers of logical reasoning to solve simpler problems like this, without formal mathematical methods. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );