= Solution
For a rate measurement of the small <mixing angle> $\theta_{13}$, choose the first fast disappearance maximum,
$$
\Delta_{23}=\frac\pi2,\qquad
\boxed{L_{\rm opt}\simeq\frac{\pi E}{2k_{\rm practical}|\Delta m_{23}^2|}=1.24\ \mathrm{km}\quad(E=3\ \mathrm{MeV}).}
$$
A 47 km baseline instead lies near the slow <oscillation> maximum associated with $\theta_{12}$. Its much lower flux, approximately falling as $1/L^2$, and the many fast <oscillations> washed out by a reactor's broad <energy> spectrum make it a poor choice for this simple $\theta_{13}$ design. A medium-baseline spectral experiment can still constrain <neutrino oscillation> parameters if it has enough events and resolution; 47 km is not intrinsically useless, but it is not the optimal short-baseline rate experiment. In <6/a>, $\theta_{13}$ also affects the slow envelope through $\cos^4\theta_{13}$, so the sensitivity there is not identically zero.
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