Enclosing playing field

Question

You have 600 meters of fencing, and you plan to lay out two identical playing fields. The fields can be side by side and separated by a fence. Find the dimensions and the maximum area of each field.

Answer 1

draw a rectangle and label width x and height y

xy = A is what we are maximizing

However, we only have 600 = 2x + 3y since we have a fence in the middle

solve 600 = 2x+3y for either x or y.

plug that equation into xy = A

Now we have a function A(y) or A(x)

Derive A(y) or A(x) and set the derivative equal to 0, then solve for x or y