An area model for a fenced pen

A farmer uses \(30\) m of fencing to make three sides of a rectangular pen against a long wall. The two sides at right angles to the wall are each \(x\) m long.

1. Show that the area of the pen, \(A\text{ m}^2\), is given by \(A=x(30-2x)\).
2. Find the values of \(x\) for which the area is \(100\text{ m}^2\).
3. Explain why \(x\) must lie between \(0\) and \(15\).
4. Use the symmetry of the graph of \(A\) against \(x\) to find the greatest possible area.