document.write( "Question 990404: The perimeter of a rectangle is 72cm. If the length is increased by 20% and the width is decreased by 25% the perimeter remains the same . calculate the length and width of the original rectangle \n" ); document.write( "
Algebra.Com's Answer #610461 by MathTherapy(10552)\"\" \"About 
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\n" ); document.write( "The perimeter of a rectangle is 72cm. If the length is increased by 20% and the width is decreased by 25% the perimeter remains the same . calculate the length and width of the original rectangle
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Let original length and width be L, and W, respectively
\n" ); document.write( "Then: Perimeter = 2(L + W) --------> 2(L + W) = 72 ------- 2(L + W) = 2(36) ------> L + W = 36______W = 36 - L
\n" ); document.write( "Increasing length by 20% makes new length: 1.2L
\n" ); document.write( "Decreasing width by 25% makes new width: .75(36 - L), or 27 - .75L
\n" ); document.write( "We then get: 2(1.2L) + 2(27 - .75L) = 72
\n" ); document.write( "2.4L + 54 - 1.5L = 72
\n" ); document.write( "2.4L - 1.5L = 72 - 54
\n" ); document.write( ".9L = 18
\n" ); document.write( "L, or original length = \"18%2F.9\", or \"highlight_green%2820%29\" cm
\n" ); document.write( "Original width: 36 - 20, or \"highlight_green%2816%29\" cm \n" ); document.write( "
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