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.(1 point)
Responses
5m
12m
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, then the new side length will be (x + 3) and the new area 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 quadratic equation, we get (x + 12)(x - 6) = 0.
Therefore, the potential solutions are x = -12 and x = 6. However, the length of a side cannot be negative, so x = 6 meters.
Therefore, the length of each side of the original garden is 6 meters.
Correct Response: 6m