High-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>T</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:math>ferromagnetic inverse Heusler alloys: A comparative study of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">Fe</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mi>RhSi</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">Fe</mml:mi><mml:mn>2</mml:mn></mml:msub><…

We report the results of experimental investigations on structural, magnetic, resistivity, caloric properties Fe$_2$RhZ (Z=Si,Ge) along with \textit{ab-initio} band structure calculations using first principle simulations. Both these alloys are found to crystallize in inverse Heusler but disorder tetrahedral sites between Fe and Rh. Fe$_2$RhSi has saturation moment 5.00 $\mu_B$ while its counterpart 5.19 $\mu_B$. Resistivity measurement reveals metallic nature both them. Theoretical simulations generalized gradient approximation(GGA) predict ferromagnetic ordering as ground state for alloys. However it underestimates experimentally observed moments. GGA+$U$ approach, Hubbard $U$ values estimated from density functional perturbation theory helps improve comparison results. is be half ferromagnet Fe$_2$RhGe not. Varying Rh does not change net much Fe$_2$RhSi, unlike Fe$_2$RhGe. Relatively small exchange splitting orbitals compared that reason opening gap minority spin channel former. High temperature make useful spintronics applications.