document.write( "Question 706441: A rectangular picture is 3 cm longer than it is wide. The picture is surrounded by a frame that is 2 cm wide. The area of the picture and the frame together is 1000cm^ greater than the area of the picture. I need to find the width of the picture. \n" ); document.write( "
Algebra.Com's Answer #435266 by ankor@dixie-net.com(22740)\"\" \"About 
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A rectangular picture is 3 cm longer than it is wide.
\n" ); document.write( " The picture is surrounded by a frame that is 2 cm wide.
\n" ); document.write( " The area of the picture and the frame together is 1000cm^ greater than the area of the picture.
\n" ); document.write( " I need to find the width of the picture.
\n" ); document.write( ":
\n" ); document.write( "let w = the width of the picture
\n" ); document.write( "then
\n" ); document.write( "(w+3) = the length of the picture
\n" ); document.write( "and
\n" ); document.write( "w(w+3) = w^2 + 3w; the area of the picture
\n" ); document.write( ":
\n" ); document.write( "The overall area; add 4 cm to the length and the width of picture
\n" ); document.write( "W = (w+4)
\n" ); document.write( "L = (w+7)
\n" ); document.write( "A = (w+4)(w+7) = w^2 + 11w + 28; the overall area of the frame and picture
\n" ); document.write( ":
\n" ); document.write( "Overall area - picture area = 1000 cu/cm
\n" ); document.write( "w^2 + 11w + 28 -(w^2 + 3w) = 1000
\n" ); document.write( "combine like terms
\n" ); document.write( "w^2 - w^2 + 11w - 3w = 1000 - 28
\n" ); document.write( "8w = 972
\n" ); document.write( "w = 972/8
\n" ); document.write( "w = 121.5 cm is the width of the picture
\n" ); document.write( "then
\n" ); document.write( "121.5 + 3 = 124.5 cm is the length of the picture
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "YOu can check this: (125.5*128.5) - (121.5*124.5) = \n" ); document.write( "
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