We attempt to study a singularity-free model for the spherically symmetric anisotropic strange stars under Einsteins general theory of relativity by exploiting the Tolman-Kuchowicz metric. Further, we have assumed that the cosmological constant $Lambda$ is a scalar variable dependent on the spatial coordinate $r$. To describe the strange star candidates we have considered that they are made of strange quark matter (SQM) distribution, which is assumed to be governed by the MIT bag equation of state. To obtain unknown constants of the stellar system we match the interior Tolman-Kuchowicz metric to the exterior modified Schwarzschild metric with the cosmological constant, at the surface of the system. Following Deb et al. we have predicted the exact values of the radii for different strange star candidates based on the observed values of the masses of the stellar objects and the chosen parametric values of the $Lambda$ as well as the bag constant $mathcal{B}$. The set of solutions satisfies all the physical requirements to represent strange stars. Interestingly, our study reveals that as the values of the $Lambda$ and $mathcal{B}$ increase the anisotropic system becomes gradually smaller in size turning the whole system into a more compact ultra-dense stellar object.
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