  The present work is focused on the investigation of the existence of compact
structures describing anisotropic matter distributions within the framework of
modified gravity theories, specifically f(R,$\mathcal{T}$) gravity theory.
Additionally, we have taken f(R,$\mathcal{T}$) as a linear function of the
Ricci scalar $R$ and the trace of the energy-momentum tensor $\mathcal{T}$ as
$f(R,\mathcal{T})$=$R+2\chi\mathcal{T}$,where $\chi$ is a dimensionless
coupling parameter, and the Lagrangian matter
$\mathcal{L}_m=-\frac{1}{3}\left(2p_{t}+p_{r}\right)$, to describe the complete
set of field equations for the anisotropic matter distribution. We follow the
embedding class one procedure using Eisland condition to obtain a full
space-time description inside the stellar configuration. Once the space-time
geometry is specified we determine the complete solution of the modified
Einstein equations by using the MIT bag model equation of state
$p_{r}=\frac{1}{3}\left(\rho-4B\right)$ that describes the strange quark matter
(SQM) distribution inside the stellar system, where $B$ denotes a bag constant.
The physical validity of our anisotropic solution is confirmed by executing
several physical tests. It is worth mentioning that with the help of the
observed mass values for the various strange star candidates we have predicted
the exact radii by taking different values for $\chi$ and $B$. These predicted
radii show monotonic decreasing nature as the parameter $\chi$ is moved from
$-0.8$ to $0.8$ progressively. In this case, our anisotropic stellar system
becomes more massive and transforms into more dense compact stars.
