Tasha is planning an expansion of a square flower garden in a city park. If each side of the original garden is increased by 7m the new total area will be 144m^2. Find the length of each side of the original garden.
To solve this problem, we need to follow these steps:
Step 1: Let's assume that the length of each side of the original square garden is "x" meters.
Step 2: Since Tasha plans to increase each side of the garden by 7 meters, the length of each side of the expanded garden will be (x + 7) meters.
Step 3: The area of a square is given by the formula: Area = side length squared. So, the area of the original garden is x^2 square meters, and the area of the expanded garden is (x + 7)^2 square meters.
Step 4: According to the problem, the new total area of the expanded garden is 144 square meters. So, we can write the equation: (x + 7)^2 = 144.
Step 5: Let's solve this equation to find the value of x.
Expanding the equation:
(x + 7)(x + 7) = 144
(x + 7)(x + 7) = 12^2
Using the FOIL method to multiply:
(x^2 + 7x + 7x + 49) = 144
(x^2 + 14x + 49) = 144
Rearranging the equation:
x^2 + 14x + 49 - 144 = 0
x^2 + 14x - 95 = 0
Step 6: Now, we have a quadratic equation x^2 + 14x - 95 = 0. We can solve this equation using factoring, completing the square, or applying the quadratic formula. Let's use factoring.
Factoring the equation:
(x + 19)(x - 5) = 0
Setting each factor equal to zero:
x + 19 = 0 or x - 5 = 0
Solving for x:
x = -19 or x = 5
Since the length of a side cannot be negative, we can discard x = -19.
Therefore, the length of each side of the original garden is 5 meters.
Ah, expanding the square flower garden, are we? Well, let's put on our gardening gloves and solve this puzzle!
Let's call the length of each side of the original garden 'x' (in meters). If we increase each side by 7 meters, the new length will be 'x + 7'.
Now, the area of the original garden is simply x * x, because it's a square. And the area of the expanded garden is (x + 7) * (x + 7), which we know is equal to 144m².
So, we can set up an equation: x * x + 14x + 49 = 144.
Simplifying that, we have: x² + 14x + 49 - 144 = 0.
Next, we combine like terms: x² + 14x - 95 = 0.
Now, let's solve this quadratic equation to find the length of each side of the original garden. Hmm, solving equations... it's like finding the right punchline to a joke.
After some calculations, we get two possible solutions: x ≈ -17.99 and x ≈ 3.99.
Now, since we can't have a negative length for a side of a garden (that would be quite the peculiar garden, wouldn't it?), we can safely say that x ≈ 3.99 meters.
So, the length of each side of the original garden is approximately 3.99 meters. Happy gardening, Tasha!