The maximum area is
[tex]100\times33\frac{1}{3}ft^2[/tex]Explanation:Let the playground be demonstrated as follows:
The perimeter of a rectangle is:
P = 2x + 3y
This is given as 400, so
2x + 3y = 400
y = (400 - 2x)/3
Area = x * y
= x * (400 - 2x)/3
[tex]A=-\frac{2}{3}x^2+\frac{400}{3}x[/tex]Maximum is dA/dx = 0
[tex]\begin{gathered} -\frac{4}{3}x+\frac{400}{3}=0 \\ \\ -4x+400=0 \\ x=\frac{400}{4}=100 \end{gathered}[/tex]2x + 3y = 400
2(100) + 3y = 400
3y = 400 - 200
3y = 100
y = 100/3 = 33 1/3
The maximum area is 100 * 33 1/3
