document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=41196>Question 41196</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A picture frame is 20 inches by 12 inches. There are 84inches^2 of the picture showing. Find the width of the frame.<BR>\n" );
document.write( "___ inches<BR>\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26602 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=26602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the width of the frame be x.  Let the dimensions of just the picture be L and W.  Thus we know <BR>\n" );
document.write( "A = LW = 84<BR>\n" );
document.write( "We also know that<BR>\n" );
document.write( "(L + 2x)(W + 2x) = 240<BR>\n" );
document.write( "We also know that<BR>\n" );
document.write( "L + 2x = 20<BR>\n" );
document.write( "W + 2x = 12<BR>\n" );
document.write( "Let us solve these for L and W and plug in to the first equation, so we get<BR>\n" );
document.write( "L = 20 - 2x<BR>\n" );
document.write( "W = 12 - 2x<BR>\n" );
document.write( "and then<BR>\n" );
document.write( "(20 - 2x)(12 - 2x) = 84<BR>\n" );
document.write( "240 - 64x + 4x^2 = 84<BR>\n" );
document.write( "4x^2 - 64x + 156 = 0<BR>\n" );
document.write( "x^2 - 16x + 39 = 0 <BR>\n" );
document.write( "(x - 13)(x - 3) = 0<BR>\n" );
document.write( "x = 13 or x = 3<BR>\n" );
document.write( "but x cannot be 13, so<BR>\n" );
document.write( "x = 3  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );