document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186641>Question 1186641</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a picture frame on colored cardboard 40 cm by 32cm. if there is a uniform border around the picture such that area of the border is 720 cm2.find the length and width of the picture. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #817585 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=817585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The cardboard is 8cm longer than it is wide.  Since the border is uniform, the picture itself is 8cm longer than it is wide.<br><BR>\n" );
document.write( "The area of the cardboard is 40*32=1280 cm^2; the area of the border is 720 cm^2.  So the area of the picture is 1280-720=560 cm^2.<br><BR>\n" );
document.write( "Let x be the width of the picture; then x+8 is the length.  Since the area is 560...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B8%29=560 ALIGN=MIDDLE  ALT=\"x%28x%2B8%29=560\"   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%2B8x=560 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x=560\"   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%2B8x-560=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x-560=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%2B28%29%28x-20%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B28%29%28x-20%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "x=-28 or x=20<br><BR>\n" );
document.write( "Obviously the negative answer makes no sense in the problem.  So x=20.<br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "picture width: x=20cm<BR>\n" );
document.write( "picture length: x+8=28cm<br><BR>\n" );
document.write( "Note in solving the problem using formal algebra we had to factor a quadratic expression by finding two numbers whose difference is 8 and whose product is 560.  That's what the original problem required us to do; so the formal algebra didn't get us any closer to the answer.<br><BR>\n" );
document.write( "Trial and error and a bit of mental arithmetic will get us to the solution quickly:<BR>\n" );
document.write( "560=56*10 no...<BR>\n" );
document.write( "560=14*40 no...<BR>\n" );
document.write( "560=28*20 YES!<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );