The area of a playground is 216 yd2. The width of the playground is 6 yd longer than its length. Find the length and width of the playground, including appropriate units. Then, enter the sum of the length and width in the provided grid. Show your work
please help
w (w+6) = 216
w^2 + 6 w - 216 = 0
(w-12)(w+18) = 0
w = 12, L = 18
thank you
Let's solve this step-by-step:
Let's assume the length of the playground is x yards.
According to the given information, the width of the playground is 6 yards longer than its length.
So, the width can be represented as (x + 6) yards.
The formula to calculate the area of a rectangle is length * width.
Given that the area of the playground is 216 square yards, we can set up the equation:
x * (x + 6) = 216
Expanding the equation:
x^2 + 6x = 216
Rearranging the equation:
x^2 + 6x - 216 = 0
To solve this equation, we can factorize or use the quadratic formula. In this case, let's factorize:
(x + 18)(x - 12) = 0
Setting each factor equal to zero:
x + 18 = 0, x - 12 = 0
Solving for x, we have two possible values for the length of the playground:
x = -18 (rejecting this value) or x = 12
Since the length cannot be negative, we conclude that the length of the playground is 12 yards.
Now, to find the width of the playground, we substitute the value of x in the equation: width = x + 6.
width = 12 + 6 = 18 yards.
Therefore, the length of the playground is 12 yards and the width is 18 yards.
To solve this problem, we can set up two equations based on the given information and use them to find the length and width of the playground.
Let's represent the length of the playground as 'L' and the width as 'W.'
From the problem, we know that the area of the playground is 216 yd2:
Area = Length × Width
216 = L × W --------(equation 1)
We are also given that the width of the playground is 6 yards longer than its length:
Width = Length + 6
W = L + 6 ----------(equation 2)
We can now substitute equation 2 into equation 1 to eliminate 'W':
216 = L × (L + 6)
Expanding the equation:
216 = L^2 + 6L
Rearranging the equation to its quadratic form:
L^2 + 6L - 216 = 0
Now, we can solve this quadratic equation for L by factoring or using the quadratic formula. In this case, let's factor it:
(L - 12)(L + 18) = 0
Setting each factor to zero and solving for L:
L - 12 = 0 or L + 18 = 0
L = 12 or L = -18
Since a length cannot be negative, we discard L = -18. Therefore, the length of the playground is L = 12 yards.
Now, we can find the width by substituting the length into equation 2:
W = L + 6
W = 12 + 6
W = 18
So, the length of the playground is 12 yards, and the width is 18 yards. Adding them together, the sum is 12 + 18 = 30 yards.
Please remember to include the units when giving your answer.