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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
x = length of the sides of the original square (in centimeters).
The lengths of the sides of the rectangle will be
%28x-6%29cm and %28x-2%29cm
and the area of the rectangle (in square centimeters) would be
%28x-2%29%28x-6%29=5
We solve the quadratic equation:
%28x-2%29%28x-6%29=5 --> x%5E2-8x%2B12=5 --> x%5E2-8x%2B7=0 --> %28x-7%29%28x-1%29=5
The solution to the equation above are x=7 and x=1.
The solution to the problem is highlight%287cm%29
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 -1cm and -5cm,
which cannot be the lengths of the sides of a rectangle,
even if they multiply to yield a product of 5cm%5E2.
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