We have a given rectangular parallelepiped[tex]ABCDA_1B_1C_1D_1[/tex] with edges [tex]AB = 6[/tex], [tex]BC = 3[/tex] and [tex]AA_1 = 6[/tex]. Through the diagonal [tex]AC_1[/tex] is passing a plain, which intersects the surrounding edges [tex]BB_1[/tex] and [tex]DD_1[/tex] in the points K and L respectively. Find the section BK in the case when the area of the cut [tex]AKC_1L[/tex] is minimal.

Answer: BK = 3,84.