Answer:
The dimensions of the playground that will enclose the greatest total area are 140 ft x 210 ft.
Step-by-step explanation:
We have a rectangular with sides "a" and "b", so that the area is:

The perimiter for this rectangle is

The fence is for the perimeter plus the division, which has a length of "a".
So the total fencing is:

We can express one side in function of the other, in order to optimize the area.

Then, we can write the area as:

To maximize the area we will derive and equal to zero

Then, the value for the other side of the rectangle is:
