tasha is planning an expansion of a square of a flower garden in a city park. if each side of the original garden is increased by 7 m, the new total area of the garden will be 144 m^2. find the length of each side of the garden.
Let x be the length of each side of the original garden. Then, the area of the original garden is x^2.
If each side is increased by 7m, the new length of each side will be x+7. Therefore, the new total area of the garden will be (x+7)^2.
We are given that the new total area is 144 m^2, so we can set up the equation:
(x+7)^2 = 144
Expanding the left side, we get:
x^2 + 14x + 49 = 144
Subtracting 144 from both sides:
x^2 + 14x - 95 = 0
We can factor this quadratic equation as:
(x+19)(x-5) = 0
Therefore, the solutions are x = -19 and x = 5.
Since the length of the side of a garden cannot be negative, we can discard the solution x = -19.
Therefore, the length of each side of the original garden is x = 5m.
To check our answer, we can verify that each side of the expanded garden is 12m (5m + 7m), and the area of the expanded garden is indeed 144 m^2.