= Solution
Let $P$ be the platform's <proper length>, measured in its rest frame $S'$. At the single station-frame time $t'=0$, its ends coincide with train endpoints whose simultaneous station-frame separation is $L/\gamma$. Thus
$$
\boxed{P=\frac L\gamma=L\sqrt{1-v^2/c^2}.}
$$
The platform endpoint <world lines> are vertical at $x'=\pm P/2$ in the station <spacetime diagram>. In the train frame they are $x=-vt\pm P/(2\gamma)$, so their separation at a common train-frame time is $\boxed{P/\gamma=L/\gamma^2}$. The two alignment events lie on the tilted line $t'=0$ in the train diagram and are not simultaneous there; their separation $L$ cannot be used as the platform length measured at one train-frame time. This is the distinction enforced by <length contraction>.
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