  We analyze 221 eclipsing binaries (EBs) in the Large Magellanic Cloud with
B-type main-sequence (MS) primaries ($M_1$ $\approx$ 4 - 14 M$_{\odot}$) and
orbital periods $P$ = 20 - 50 days that were photometrically monitored by the
Optical Gravitational Lensing Experiment. We utilize our three-stage automated
pipeline to (1) classify all 221 EBs, (2) fit physical models to the light
curves of 130 detached well-defined EBs from which unique parameters can be
determined, and (3) recover the intrinsic binary statistics by correcting for
selection effects. We uncover two statistically significant trends with age.
First, younger EBs tend to reside in dustier environments with larger
photometric extinctions, an empirical relation that can be implemented when
modeling stellar populations. Second, younger EBs generally have large
eccentricities. This demonstrates that massive binaries at moderate orbital
periods are born with a Maxwellian "thermal" orbital velocity distribution,
which indicates they formed via dynamical interactions. In addition, the
age-eccentricity anticorrelation provides a direct constraint for tidal
evolution in highly eccentric binaries containing hot MS stars with radiative
envelopes. The intrinsic fraction of B-type MS stars with stellar companions
$q$ = $M_2$/$M_1$ $>$ 0.2 and orbital periods $P$ = 20 - 50 days is (7 $\pm$
2)%. We find early-type binaries at $P$ = 20 - 50 days are weighted
significantly toward small mass ratios $q$ $\approx$ 0.2 - 0.3, which is
different than the results from previous observations of closer binaries with
$P$ $<$ 20 days. This indicates that early-type binaries at slightly wider
orbital separations have experienced substantially less coevolution and
competitive accretion during their formation in the circumbinary disk.
