The isosceles right triangle conjecture for fixed-area right triangles

Let $A>0$, and consider all right triangles of area $A$. Write $\rho(\Omega)$ for the torsional rigidity of a right triangle $\Omega$.

Isosceles right triangle conjecture. Among all right triangles with area $A>0$, the one with largest torsional rigidity is the isosceles right triangle with area $A$.

The conjecture is motivated by the symmetry of other known extremal shapes and specializes to the unit-area claim discussed earlier. The source does not report a proof or disproof; its numerical study only gives approximate verification.