When is the area of a face of this pyramid a minimum?

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A pyramid of given volume \(V\) stands on a horizontal square base of edge \(2x\), and its vertex is vertically above the centre of the base. Show that the area \(A\) of a sloping triangular face is given by \[A^2=\frac{9V^2}{16x^2}+x^4,\] and prove that, as \(x\) varies, \(A\) is least when the face is equilateral.