A uniform lamina is in the form of a triangle \(A B C\), with \(A C=8 a, B C=6 a\) and angle \(A C B=90^{\circ}\). The point \(D\) on \(A C\) is such that \(A D=3 a\). The point \(E\) on \(C B\) is such that \(C E=x\) (see diagram). The triangle \(C D E\) is removed from the lamina.
(a) Find, in terms of \(a\) and \(x\), the distance of the centre of mass of the remaining object \(A D E B\) from \(A C\).

The object \(A D E B\) is on the point of toppling about the point \(E\) when the object is in the vertical plane with its edge \(E B\) on a smooth horizontal surface.
(b) Find \(x\) in terms of \(a\).