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Let us define a "rational triangle" as one in the Euclidean plane, with lengths of all sides rational.

We are aware that a positive integer is called "congruent" only if it is the area of a right triangle with rational length sides; so not every rational number is the area of some right rational triangle. However,

1. is every positive rational number the area of some (not necessarily right) rational triangle?

2. 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?

with regards,
R. Nandakumar,
K. Shesadri

Let us define a "rational triangle" as one in the Euclidean plane, with lengths of all sides rational.

We are aware that a positive integer is called "congruent" only if it is the area of a right triangle with rational length sides; so not every rational number is the area of some right rational triangle. However,

1. is every positive rational number the area of some (not necessarily right) rational triangle?

2. 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?