SOLUTION: If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm2. What were the dimensions of the original square?

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Question 94986: If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm2. What were the dimensions of the original square?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm2. What were the dimensions of the original square?
:
Let x = side of original square
Then
(x-2) = side of the new square
:
Original square area - new square area = 36
x^2 - (x-2)^2 = 36
:
x^2 - (x^2 - 4x + 4) = 36: FOILed (x-2)(x-2)
:
x^2 - x^2 + 4x - 4 = 36; removing bracket changes the signs
:
4x = 36 + 4; x^2's cancel out
:
4x = 40
:
x = 40/4
:
x = 10 cm, side of original square:
:
:
Check: 10^2 - 8^2 = 36