  We investigate, both experimentally and theoretically, the static geometric
properties of a harmonically trapped Bose-Einstein condensate of ${}^6$Li$_2$
molecules in laser speckle potentials. Experimentally, we measure the in-situ
column density profiles and the corresponding transverse cloud widths over many
laser speckle realizations. We compare the measured widths with a theory that
is non-perturbative with respect to the disorder and includes quantum
fluctuations. Importantly, for small disorder strengths we find quantitative
agreement with the perturbative approach of Huang and Meng, which is based on
Bogoliubov theory. For strong disorder our theory perfectly reproduces the
geometric mean of the measured transverse widths. However, we also observe a
systematic deviation of the individual measured widths from the theoretically
predicted ones. In fact, the measured cloud aspect ratio monotonously decreases
with increasing disorder strength, while the theory yields a constant ratio. We
attribute this discrepancy to the utilized local density approximation, whose
possible failure for strong disorder suggests a potential future improvement.
