SOLUTION: 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 c

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.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= length of the sides of the original square (in centimeters).
The lengths of the sides of the rectangle will be

and

and the area of the rectangle (in square centimeters) would be

We solve the quadratic equation:
--> --> -->
The solution to the equation above are and .
The solution to the problem is
because from a square with sides measuring 1cm
if you decrease by 2cm and 6cm the lengths of the side of such square,
you get negative measures of and ,
which cannot be the lengths of the sides of a rectangle,
even if they multiply to yield a product of .
On the other hand, a square with sides measuring 7cm can have
two of its parallel sides shortened (by 6 centimeters) to 1 cm,
and the length of its other two parallel sides shortened by 2 centimeters to 5cm,
yielding a rectangle measuring 1cm by 5cm, with an area of 5 square centimeters
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