Answer:
h = 120 ft; w = 80 ft
A = 9600 ft^2
Explanation:
Let h and w be the dimensions of the playground. The area is given by:
A = h*w (eq1)
The total amount of fence used is:
L = 2*h + 2*w + w (eq2) (an extra distance w beacuse of the division)
Solving for w:
w = L - 2/3*h = 480 - 2/3*h (eq3) Replacing this into the area eq:
[tex]A = h * (480 - 2/3*h) = 480*h - 2/3*h^2[/tex]
We derive this and equal zero to find its maximum:
[tex]dA = 480 - 4/3*h = 0[/tex] Solving for h:
h = 120 ft. Replacing this into eq3:
w = 80ft
Therefore the maximum area is:
A = 9600 ft^2
