Consider the triangles with vertices \( A(2,1) \), \( B(0,0) \) and \( C(t,4),\ t\in[0,4] \). If the maximum and the minimum perimeters of such triangles are obtained at \( t=\alpha \) and \( t=\beta \) respectively, then \( 6\alpha+21|\beta| \) is equal to __________.
