How do I calculate lenght in magnetic circuit that includes a rigid transversely magnetized permanen

I need to calculate l_M. Can I use Ampere's law?

\(H_Ml_M+H_Ll_L=0\)

and than Gauss's law \(B_LA_L=B_ML_M\)

and \(B_M=B_R+\mu H_M\)

Can I do it like this? If someone would like to finish it I would be really thankful.