  We use a statistical sample of galaxy clusters from a large cosmological
$N$-body$+$hydrodynamics simulation to examine the relation between morphology,
or shape, of the X-ray emitting intracluster medium (ICM) and the mass
accretion history of the galaxy clusters. We find that the mass accretion rate
(MAR) of a cluster is correlated with the ellipticity of the ICM. The
correlation is largely driven by material accreted in the last $\sim 4.5$~Gyr,
indicating a characteristic time-scale for relaxation of cluster gas.
Furthermore, we find that the ellipticity of the outer regions ($R\sim R_{\rm
500c}$) of the ICM is correlated with the overall MAR of clusters, while
ellipticity of the inner regions ($\lesssim 0.5 R_{\rm 500c}$) is sensitive to
recent major mergers with mass ratios of $\geq 1:3$. Finally, we examine the
impact of variations in cluster mass accretion history on the X-ray
observable-mass scaling relations. We show that there is a {\it continuous\/}
anti-correlation between the residuals in the $T_x-M$ relation and cluster
MARs, within which merging and relaxed clusters occupy extremes of the
distribution rather than form two peaks in a bi-modal distribution, as was
often assumed previously. Our results indicate the systematic uncertainties in
the X-ray observable-mass relations can be mitigated by using the information
encoded in the apparent ICM ellipticity.
