Answer:
The dimension of the playground is 60ft by 60ft and the maximum area of the playground is 3,600ft²
Explanation:
Given
A playground of 240 feet of fencing.
Required.
Dimension of the playground.
Before solving any further, it'll be assumed that the playground is a rectangular shape.
Having said this,
If the playground required 240ft of fencing, then it's perimeter is 240ft.
The perimeter of a Rectangle is;
P = 2(L + W)
Where P represents the perimeter;
L and W represent the length and the width of the rectangle respectively.
By substituting 240 for P, we have
240 = 2(L + W)
Multiply both sides by ½
½ * 240 = ½ * 2(L + W)
120 = L + W.
Make W the subject of formula
W = 120 - L ---- Equation 1.
The area of a rectangle;
A = L * W
Where A represents the area;
Substitute 120 - L for W in the above formula.
A = (120 - L) * L
A = L(120 - L)
To get an arbitrary value of L, put A = 0
So, we have:
L(120 - L) = 0
L = 0 or 120 - L = 0
L = 0 or L = 120
From the question, we are to calculate the maximum area.
The maximum area is at the mean of the arbitrary value of L
Hence, L = ½(0 + 120)
L = ½(120)
L = 60ft
Recall that W = 120 - L.
So, W = 120 - 60
W = 60ft.
Hence, the dimension of the playground is 60ft by 60ft.
Now, that we have the dimension of the playground, we can now calculate the maximum area.
Area = Length * Width
Area = 60ft * 60ft
Area = 3,600 ft²
Conclusively, the dimension of the playground is 60ft by 60ft and the maximum area of the playground is 3,600ft²