Let      and  It is proved that in a Euclidean plane, there is, up to congruence, at most one triangle  with a side of length a (resp., an angle of radian measure  area A and perimeter p. Given a  and A, necessary and sufficient conditions are given on p for the existence of such  If only A and one of  or a sufficiently large p are specified, there exist infinitely many congruence classes of triangles with the specified properties. The only prerequisites for this note are elementary analytic geometry and differential calculus.

Euclidean geometry, triangle, area, perimeter, side-length, angle, right