The resistance across M and N in the given fig. is

The resistance of each side of the triangle would be r / 2 as the two resistances are connected in parallel. The two sides are in series and hence their equivalent resistance would be (r / 2) + (r / 2) = r. This equivalent resistance is connected in parallel with third one. Hence1R=1r+1(r/2)=1r+2r=3r  or  R=r3