document.write( "Question 718481: A square is transformed into a rectangle by decreasing the length of two of its parallel sides by 6 centimeters, and by decreasing the length of its other two parallel sides by 2 centimeters. If the area of the rectangle is 5 square centimeters, find the set of all possible lengths of the sides of the original square. \n" ); document.write( "

Algebra.Com's Answer #440950 by KMST(5328) $\"\"$ $\"About$

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$\"x\"$ = length of the sides of the original square (in centimeters).
\n" ); document.write( "The lengths of the sides of the rectangle will be
\n" ); document.write( " $\"%28x-6%29\"$ $\"cm\"$ and $\"%28x-2%29\"$ $\"cm\"$
\n" ); document.write( "and the area of the rectangle (in square centimeters) would be
\n" ); document.write( " $\"%28x-2%29%28x-6%29=5\"$
\n" ); document.write( "We solve the quadratic equation:
\n" ); document.write( " $\"%28x-2%29%28x-6%29=5\"$ --> $\"x%5E2-8x%2B12=5\"$ --> $\"x%5E2-8x%2B7=0\"$ --> $\"%28x-7%29%28x-1%29=5\"$
\n" ); document.write( "The solution to the equation above are $\"x=7\"$ and $\"x=1\"$ .
\n" ); document.write( "The solution to the problem is $\"highlight%287cm%29\"$
\n" ); document.write( "because from a square with sides measuring 1cm
\n" ); document.write( "if you decrease by 2cm and 6cm the lengths of the side of such square,
\n" ); document.write( "you get negative measures of $\"-1cm\"$ and $\"-5cm\"$ ,
\n" ); document.write( "which cannot be the lengths of the sides of a rectangle,
\n" ); document.write( "even if they multiply to yield a product of $\"5cm%5E2\"$ .
\n" ); document.write( "On the other hand, a square with sides measuring 7cm can have
\n" ); document.write( "two of its parallel sides shortened (by 6 centimeters) to 1 cm,
\n" ); document.write( "and the length of its other two parallel sides shortened by 2 centimeters to 5cm,
\n" ); document.write( "yielding a rectangle measuring 1cm by 5cm, with an area of 5 square centimeters \n" ); document.write( "

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