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 225 square meters. Find the length of each side of the original garden.
A. 15 m
B. 3 m
C. 12 m****
D. Start Root 12 End Root m
Well Fiddle sticks! Seems that I am not sure if my answer is correct. Can someone double check for me? I choose C for my answer
12 works for me.
thank you
To find the length of each side of the original garden, we can use the formula for the area of a square:
Area = side length^2
Let's assume the original length of each side is x meters. According to the problem, if each side of the original garden is increased by 3 meters, the new length of each side will be (x + 3) meters.
The new total area of the garden is given as 225 square meters. We can set up the following equation:
(x + 3)^2 = 225
Expanding the equation:
x^2 + 6x + 9 = 225
Rearranging the equation:
x^2 + 6x - 216 = 0
Now we can solve this quadratic equation by factoring or using the quadratic formula. Factoring, we have:
(x - 12)(x + 18) = 0
Setting each factor equal to zero:
x - 12 = 0 or x + 18 = 0
x = 12 or x = -18
Since a negative length doesn't make sense, we can conclude that the length of each side of the original garden is 12 meters.
Therefore, your answer C is correct. Well done!
To find the length of each side of the original garden, we can use the given information.
Let's assume that the length of each side of the original garden is 'x' meters.
According to the problem, if each side is increased by 3 meters, the new total area of the garden will be 225 square meters.
So, the area of the original garden is x^2 square meters.
The area of the expanded garden is (x + 3) * (x + 3) square meters.
Given that the new total area of the garden is 225 square meters, we can set up the equation:
(x + 3) * (x + 3) = 225
Expanding this equation, we get:
x^2 + 6x + 9 = 225
Rearranging the equation, we have:
x^2 + 6x - 216 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula.
Factoring the equation, we have:
(x - 12)(x + 18) = 0
Setting each factor to zero, we get:
x - 12 = 0 or x + 18 = 0
Solving for x in each equation, we find:
x = 12 or x = -18
Since we are looking for the length of each side, which cannot be negative, we can discard the solution x = -18.
Therefore, the length of each side of the original garden is 12 meters.
So, the correct answer is C. 12 m.
Please note that answer choices given in this format can vary across different sources, so it's always a good idea to carefully follow the explanation and understand the steps to find the correct answer.