Explanation

(a) Two resistances of each side of triangle are connected in parallel. Therefore, the effective resistance of each arm of the triangle would be $= \frac{r \times r}{r + r} = \frac{r}{2}$. The two arms$\ AB$
and$\ AC$ are in series and they together are in parallel with third one.
$\therefore\ \ R^{'}(r/2) + (r/2) = r$
Total resistance
$\frac{1}{R} = \frac{1}{r} + \frac{2}{r} = \frac{3}{r}$
$R = r/3$