  Given any positive integer $n$, it is well-known that there always exists a
triangle with rational sides $a,b$ and $c$ such that the area of the triangle
is $n$. For a given prime $p \not \equiv 1$ modulo $8$ such that $p^{2}+1=2q$
for a prime $q$, we look into the possibility of the existence of the triangles
with rational sides with $p$ as the area and $\frac{1}{p}$ as $\tan
\frac{\theta}{2}$ for one of the angles $\theta$. We also discuss the relation
of such triangles with the solutions of certain Diophantine equations.
