12. A community group is planning the expansion of a square flower garden in a city park if each side of the original garden is increased by 3 meters, the new total area of the garden will be 81 square meters. Find the length of each side of the original garden.
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Let x be the length of each side of the original garden.
The original area of the garden is x^2 square meters.
The new area of the garden is (x + 3)^2 = x^2 + 6x + 9 square meters.
Since the new total area of the garden will be 81 square meters, we can set up the equation:
x^2 + 6x + 9 = 81
Solving for x:
x^2 + 6x - 72 = 0
(x + 12)(x - 6) = 0
x = 6 or x = -12
Since the length of a side cannot be negative, the length of each side of the original garden is 6 meters.