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

Question 78507: If the sides of a square are decreased by 2 cm., the area is decreased by 36 cm^2. What were the dimensions of the original square?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If the sides of a square are decreased by 2 cm., the area is decreased by 36 cm^2. What were the dimensions of the original square?
:
Let x^2 = the area of the original square:
Then (x-2)^2 = area of the smaller square:
:
Large square area - small square area = 36
x^2 - (x-2)^2 = 36
:
FOIL (x-2)(x-2):
x^2 - (x^2 - 4x + 4) = 36
:
Remove brackets, changes the signs inside the brackets:
x^2 - x^2 + 4x - 4 = 36
4x = 36 + 4
4x = 40
x = 40/4
x = 10 cm, side of original square
:
:
Check:
10^2 - 8^2 =
100 - 64 = 36

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