document.write( "Question 1155671: 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. \n" ); document.write( "
Algebra.Com's Answer #778302 by josmiceli(19441)\"\" \"About 
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The area of picture and frame is:
\n" ); document.write( "\"+40%2A60+=+2400+\" cm2
\n" ); document.write( "Let \"+A+\" = the area of the picture
\n" ); document.write( "\"+2400+-+A+\" = the area of the frame
\n" ); document.write( "--------------------------------------------
\n" ); document.write( "\"+2400+-+A+=+2A+\"
\n" ); document.write( "\"+3A+=+2400+\"
\n" ); document.write( "\"+A+=+800+\" cm2
\n" ); document.write( "-------------------------
\n" ); document.write( "Let \"+W+\" = the width of the frame
\n" ); document.write( "\"+%28+40+-+2W+%29%2A%28+60+-+2W+%29+=+800+\"
\n" ); document.write( "\"+2400+-+120W+-+80W+%2B+4W%5E2+=+800+\"
\n" ); document.write( "\"+4W%5E2+-+200W+%2B+1600+=+0+\"
\n" ); document.write( "\"+W%5E2+-+50W+%2B+400+=+0+\"
\n" ); document.write( "\"+%28+W+-+10+%29%2A%28+W+-+40+%29+=+0+\"
\n" ); document.write( "\"+W+\" can't be \"+40+\" since that is one of
\n" ); document.write( "the outside dimensions, so
\n" ); document.write( "\"+W+=+10+\"
\n" ); document.write( "The width is 10 cm
\n" ); document.write( "--------------------------
\n" ); document.write( "check:
\n" ); document.write( "\"+%28+40+-+2W+%29%2A%28+60+-+2W+%29+=+800+\"
\n" ); document.write( "\"+%28+40+-+2%2A10+%29%2A%28+60+-+2%2A10+%29+=+800+\"
\n" ); document.write( "\"+%28+40+-+20+%29%2A%28+60+-+20+%29+=+800+\"
\n" ); document.write( "\"+20%2A40+=+800+\"
\n" ); document.write( "\"+800+=+800+\"
\n" ); document.write( "OK
\n" ); document.write( "
\n" );