document.write( "Question 1067623: The perimeter of a rectangle is 30 cm. If its length is decreased by 3 cm and its width is increased by 5 cm, the area of the rectangle will decrease by 8 cm^2. Find the area of the original rectangle.\r
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Algebra.Com's Answer #682772 by LinnW(1048)\"\" \"About 
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let a = area
\n" ); document.write( "let l = length
\n" ); document.write( "let w = width
\n" ); document.write( "Since the perimeter is 30,
\n" ); document.write( "2w + 2l = 30
\n" ); document.write( "divide each side by 2
\n" ); document.write( "w + l = 15
\n" ); document.write( "add - l to each side
\n" ); document.write( "w = 15 - l
\n" ); document.write( "Below we see ( length - 3 )(width + 5) = original area - 8
\n" ); document.write( "(l-3)(w+5)=a-8\r
\n" ); document.write( "\n" ); document.write( "Since lw = a ,\r
\n" ); document.write( "\n" ); document.write( "(l-3)(w+5)=lw-8\r
\n" ); document.write( "\n" ); document.write( "lw + 5*l -3*w -15 = lw -8
\n" ); document.write( "add -lw to each side
\n" ); document.write( "5*l -3*w -15 = -8
\n" ); document.write( "add 15 to each side
\n" ); document.write( "5*l -3*w = 7
\n" ); document.write( "since w = 15 - l, substitute 15 - l for w in 5*l -3*w = 7
\n" ); document.write( "5*l -3*(15 - l) = 7
\n" ); document.write( "5*l -45 + 3*l = 7
\n" ); document.write( "8*l -45 = 7
\n" ); document.write( "add 45 to each side
\n" ); document.write( "8*l = 52
\n" ); document.write( "divide each side by 8
\n" ); document.write( "l = 52/8 = 6.5
\n" ); document.write( "since w = 15 - l, w = 15 - 6.5 = 8.5
\n" ); document.write( "The area of the original rectangle = 6.5 * 8.5 = 55.25
\n" ); document.write( "Notice that area of the alternate rectangle is
\n" ); document.write( "(length -3)(width + 5) = 3.5 * 13.5 = 47.25
\n" ); document.write( "The difference in the area of the rectangles is 55.25-47.25 = 8
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