  A positive integer that is the area of some rational right triangle is called
a congruent number. In an algebraic point of view, being a congruent number
means satisfying a system of equations. As early as the 1800s, it is understood
that if $n$ is a congruent number, then the equation $nm^2 = uv(u^2 - v^2)$ has
a solution in $\mathbb{Z}$. Using the relation between congruent numbers and
elliptic curves $E_n: y^2 = x^3 - n^2 x$ which was established in the 1900s, we
will prove that the converse of this two century-old result holds as well. In
addition to this, we present another proof of the converse using the method of
2-descent. Towards the end of this paper, we demonstrate how one can use our
proof to construct subfamilies of $E_n$ with rank at least 2 and 3.
