Tasha is planning an expansion of a square 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 m². Find the length of each side of the original garden
Let x be the length of each side of the original garden.
The original area of the garden is x^2.
After increasing each side by 7m, the new area of the garden is (x+7)^2.
According to the information given, the new total area of the garden will be 144 m²:
(x+7)^2 = 144
Expanding the left side:
x^2 + 14x + 49 = 144
Subtracting 144 from both sides:
x^2 + 14x + 49 - 144 = 0
x^2 + 14x - 95 = 0
Now we need to solve this quadratic equation for x. We can do this by factoring or by using the quadratic formula.
Factoring:
(x + 19)(x - 5) = 0
x = -19 or x = 5
Since the length of a side cannot be negative, we conclude that x = 5.
Therefore, the length of each side of the original garden is 5 meters.