  IM Per is a triple star system whose eclipsing pair masses and radii are
accurate to within 1 \%. The TESS light curve of the program target exhibits
partial eclipses and multiple oscillations with mmag-level amplitudes. It is
found that the oscillations affect eclipse timing measurements. Binary modeling
of the high-quality TESS data indicates that the eclipsing components of the
triple system are twin dwarfs with parameters of $M_2$/$M_1$ = 0.995,
$R_2$/$R_1$ = 0.901, and $\Delta$($T_{\rm eff,1}$--$T_{\rm eff,2}$) = 12 K in
an eccentric ($e$ = 0.049), detached configuration. The third light of $l_3$ =
0.054 may mostly come from a G-type tertiary companion. Our predicted parallax
of 1.52 $\pm$ 0.09 mas is concurrent with the Gaia measurement of 1.52 $\pm$
0.05 mas. Multifrequency analysis of the outside-eclipse residuals reveals 22
significant pulsation signals: four in the gravity-mode region (0.03$-$2.22
day$^{-1}$) and 18 in the pressure-mode region (9.19$-$25.12 day$^{-1}$). Of
the low frequencies, $f_{11}$ and $f_{14}$ are orbital harmonics that can be
identified as tidally excited modes. The pulsation periods and constants for
the high frequencies, and the position in the Cepheid instability strip
demonstrate that the pulsating component of IM Per is a $\delta$ Sct variable.
