I always wonder about this sort of problem. It does NOT require calculus. It's great to remember your analytic geometry and check it for yourself.

A = x(30-x)

Let's recognize this as a downward-opening parabola.

Zeros: A(0) = 0 and A(30) = 0

What do we know about the relationship of the vertex and the zeros of a downward-opening parabloa.

Vertex: x = (30 + 0) / 2 = 15

A(15) = 225

Is there still a question? You MUST develop some confidence. Go carefully and confidently. Find a way to check your work. Imagine a different method, as shown here, or write so that you can verify your result. Give up guessing - trust me on this.