document.write( "Question 250461: Originally the dimensions of a rectangle were 20 cm by 23 cm. When both dimensions were decreased by the same amount, the area of the rectangle decreased by 120 cm (squared). Find the dimensions of the new rectangle. \n" ); document.write( "

Algebra.Com's Answer #185082 by drk(1908) $\"\"$ $\"About$

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We reduce length and width by the same amount to get
\n" ); document.write( "(20-X) and (23-x). Now the area is reduced by 120, so,
\n" ); document.write( " $\"460+-+%2820-X%29%2823-X%29+=+120\"$
\n" ); document.write( "foiling the left gives us
\n" ); document.write( " $\"460+-+%28x%5E2+-+43X+%2B+460%29+=+120\"$
\n" ); document.write( " $\"-x%5E2+%2B+43X+-+120+=+0+\"$
\n" ); document.write( "or
\n" ); document.write( " $\"x%5E2+-+43X+%2B+120+=+0+\"$
\n" ); document.write( "by factoring, we get
\n" ); document.write( " $\"%28x-3%29%28x-40%29+=+0\"$
\n" ); document.write( "X = 3 or X = 40.
\n" ); document.write( "Since 40 is too big,
\n" ); document.write( " we are left with X = 3.
\n" ); document.write( "The new rectangle dimensions are:
\n" ); document.write( "17 x 20 \n" ); document.write( "

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