A playground is to be constructed at the back of a daycare center using 164 feet of fencing. The back of the building will serve as one of the long sides of the playground. The playground is to have a length 6 feet longer than its width. Find the dimensions of the playground
L + 2 w = 164
but L = w + 6
so
w + 6 + 2 w = 164
Width = X feet.
Length = x+6 feet.
x + (x+6) + x = 164.
X = 52 2/3 Ft.
x+6 = 52 2/3 + 6 = 58 2/3 Ft.
To find the dimensions of the playground, we need to set up an equation based on the given information.
Let's assume that the width of the playground is "x" feet.
According to the problem, the length of the playground will be 6 feet longer than its width. So, the length can be represented as "x + 6" feet.
Now, the total fencing required to enclose the playground consists of three sides, as one side is already formed by the back of the building. We have 164 feet of fencing available for these three sides.
Hence, the equation can be set up as:
Width + Length + Width = 164
Simplifying the equation:
x + (x + 6) + x = 164
3x + 6 = 164
3x = 164 - 6
3x = 158
x = 158 / 3
x ≈ 52.67
Since we cannot have a decimal value for the width, let's round it to the nearest whole number:
x ≈ 53
Therefore, the width of the playground is approximately 53 feet. As the length is 6 feet longer than the width, the length is approximately 59 feet (53 + 6).
So, the dimensions of the playground are approximately 53 feet by 59 feet.