Quadratic Functions, Equations and Inequalities - Completing the Square and Vertex Form

A farmer wants to fence a rectangular plot of land along a straight river. He has 100 meters of fencing material and will not fence the side along the river. The rectangular plot has a length of \(y\) m and breadth of \(x\) m as shown in the diagram below.

1. Show that the area of the fenced plot of land, \(A=100x-2{{x}^{2}}\).
2. Express \(A\) in form of \(y=a{{\left( x-h \right)}^{2}}+k\) where \(a\), \(h\) and \(k\) are constants to be determined.
3. Determine the maximum possible area the farmer can enclose.