SOLUTION: If two opposite sides of a square are increased by 7 meters and the other sides are decreased by 5 meters, the area of the rectangle that is formed is 64 square meters. Find the ar

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Question 1176895: If two opposite sides of a square are increased by 7 meters and the other sides are decreased by 5 meters, the area of the rectangle that is formed is 64 square meters. Find the area of the original square.
Answer by ikleyn(52900) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the original side of the square measure.


Then from the condition, you have this quadratic equation for the new area


    (x+7)*(x-5) = 64.



From this point, you can easily guess the solution  x+7 = 16,  x = 16-7 = 9 and 

then CHECK  (9+7)*(9-5) = 16*4 = 64.



Alternatively, you can solve equation (*) formally


    x^2 + 2x - 35 - 64 = 0

    x^2 + 2x - 99 = 0

    (x+11)*(x-9) = 0    etc.

Solved.