2016 SAJC H1 Q4

The diagram shows a cardboard \(ABC\) in the shape of an equilateral triangle of side \(y\) cm. A smaller equilateral triangle \(ADE\) of side \(x\)cm is cut from the cardboard. The perimeter of the remaining cardboard \(BCED\) is \(10\)cm.

1. Show that the area of the remaining cardboard, \(A\)cm\(^{2}\), is given by
   \(\frac{\sqrt{3}}{9}(25+5x-2{{x}^{2}})\)[5]
2. Without the use of a calculator, find the maximum value of \(A\) as \(x\) varies, justifying that this value is a maximum.[3]