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Two queries on triangles, the sides of which have rational lengths

for two given rational numbers $A$ and $P$, among the infinitely many general triangles with area $A$ and perimeter $P$ (there are infinitely many such triangles if $A$ and $P$ are within a suitable range … ), is there a guarantee that there are any (or infinitely many) rational triangles? …
R. Nandakumar's user avatar