document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198912>Question 198912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A picture frame dimesions are 20cm by 30cm. If a mat was put inside the frame that decreases the picture area by 264cm^2, how wide is the mat? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149417 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=149417\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A picture frame dimensions are 20cm by 30cm. If a mat was put inside the frame<BR>\n" );
document.write( " that decreases the picture area by 264cm^2, how wide is the mat?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = width of the mat<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the overall area of the picture and frame:<BR>\n" );
document.write( "20 * 30 = 600 sq/cm<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The dimension of the picture inside the mat<BR>\n" );
document.write( "(20-2x)by(30-2x)<BR>\n" );
document.write( "Foil to find the area:<BR>\n" );
document.write( "A = 600 - 100x + 4x^2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Overall area - picture area = 264 sq/cm<BR>\n" );
document.write( "600 - (4x^2 - 100x + 600) = 264<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Remove the brackets (change signs) arrange as a quadratic eq<BR>\n" );
document.write( "-4x^2 + 100x + 600 - 600 - 264 = 0<BR>\n" );
document.write( "-4x^2 + 100x - 264 = 0<BR>\n" );
document.write( "Multiply eq by -1<BR>\n" );
document.write( "4x^2 - 100x + 264 = 0<BR>\n" );
document.write( "Simplify divide by 4<BR>\n" );
document.write( "x^2 - 25x + 66 = 0<BR>\n" );
document.write( "Factor<BR>\n" );
document.write( "(x - 22)(x - 3) = 0<BR>\n" );
document.write( "Reasonable solution<BR>\n" );
document.write( "x = 3 cm is the width of the mat<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution<BR>\n" );
document.write( "Find the area of the picture (2x=6), subtract from the overall dimensions<BR>\n" );
document.write( "14 * 24  = 336<BR>\n" );
document.write( "then<BR>\n" );
document.write( "600 - 336 = 264; confirms our solution </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );