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 169 m^2. Find the length of each side of the original garden. 13 m m 20 m 6 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 is increased by 7m, the new length of each side will be x + 7.
Therefore, the new area of the garden will be (x + 7)^2.
Given that the new total area is 169m^2, we can set up the equation:
(x + 7)^2 = 169
Expand the left side:
x^2 + 14x + 49 = 169
Subtract 169 from both sides:
x^2 + 14x - 120 = 0
Factor the quadratic equation:
(x + 20)(x - 6) = 0
Setting each factor to zero:
x + 20 = 0 or x - 6 = 0
x = -20 or x = 6
Since the side length cannot be negative, the original garden had a side length of x = 6m.
Therefore, the length of each side of the original garden is 6m.