A piece of wire, \(100\) cm in length, is divided into two parts. One part is bent to form an equilateral triangle of side \(x\) cm and the other is bent to form a square of side \(y\) cm.
Express \(y\) in terms of \(x\) and hence show that \(\quantity{A}{cm^2}\), the total area enclosed by the two shapes, is such that \[ A=\frac{\sqrt{3}x^2}{4}+\frac{(100-3x)^2}{16}. \] Calculate the value of \(x\) for which \(A\) has a stationary value. Determine whether this value of \(x\) makes \(A\) a maximum or a minimum.
