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. (1 point) Responses 19 m 19 m 12 m 12 m 5 m 5 m m Image with alt text: radical 5 m
Let x be the length of each side of the original garden.
The area of the original garden is x^2.
If each side of the original garden is increased by 7m, the new side length will be x + 7.
The new total area of the garden will be (x + 7)^2.
According to the problem, the new total area is 144m^2. So we have:
(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
Factors of -95 that sum to 14 are 19 and -5:
(x + 19)(x - 5) = 0
This leads to x = 5 (since side length cannot be negative).
Therefore, the length of each side of the original garden is 5m.