document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155671>Question 1155671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A frame of uniform width is to be placed around a painting so that the area of the frame is twice the area of the picture. If the outside dimensions of the frame of 40cm and 60cm, then find the width of the frame. </SPAN>\n" );
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document.write( "The dimensions including the frame are 40 by 60.<br><BR>\n" );
document.write( "With a frame of uniform width x, the dimensions of the painting alone are (40-2x) by (60-2x).<br><BR>\n" );
document.write( "The area of the frame is twice the area of the painting; that means the area with the frame is 3 times the area of the painting alone.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2A40+=+3%2860-2x%29%2840-2x%29 ALIGN=MIDDLE  ALT=\"60%2A40+=+3%2860-2x%29%2840-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve using basic algebra....<br><BR>\n" );
document.write( "If a formal algebraic solution is not required, the problem can be solved mentally in a few seconds.<br><BR>\n" );
document.write( "With the frame, the area is 40*60 = 2400.  That is the product of two numbers whose difference is 20 with a product of 2400.<br><BR>\n" );
document.write( "The area of the painting alone is one-third of the total area, which is 800.<br><BR>\n" );
document.write( "With a frame of uniform width, the dimensions of the painting are two numbers whose difference is also 20.<br><BR>\n" );
document.write( "A couple of moments of mental arithmetic find the dimensions of the painting to be 20 by 40.<br>\r<BR>\n" );
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