  The aim of this note is to give two new conceptual proofs of
Ionescu-Weitzenb\"ock's inequality. The first one, which is a vector proof,
provides us a geometric interpretation of the difference between the two sides
of this inequality and of two known corollary inequalities in differential
geometry. Through a less classical approach, our second proof makes use of the
properties of the set of triangles with a fixed "size", seen as a half-disk.
