  It is well known that there is a bijective correspondence between metric
ribbon graphs and compact Riemann surfaces with meromorphic Strebel
differentials. In this article, it is proved that Grothendieck's correspondence
between dessins d'enfants and Belyi morphisms is a special case of this
correspondence. For a metric ribbon graph with edge length 1, an algebraic
curve over $\bar Q$ and a Strebel differential on it is constructed. It is also
shown that the critical trajectories of the measured foliation that is
determined by the Strebel differential recover the original metric ribbon
graph. Conversely, for every Belyi morphism, a unique Strebel differential is
constructed such that the critical leaves of the measured foliation it
determines form a metric ribbon graph of edge length 1, which coincides with
the corresponding dessin d'enfant.
