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.(2 points)
Responses
5m
5m
12m
12m
3m
3m
6m
Let x be the length of each side of the original garden.
The area of the original garden is x^2.
If each side is increased by 3 meters, the new total area of the garden will be (x+3)^2 = 81.
Expanding this equation, we get x^2 + 6x + 9 = 81.
Subtracting 81 from both sides, we get x^2 + 6x - 72 = 0.
Factoring this equation, we get (x + 12)(x - 6) = 0.
This gives us two possible solutions: x = -12 or x = 6. Since the length of a side cannot be negative, the original length of each side is 6 meters.
Therefore, the correct answer is: 6m