3. If the three sides of a right-angled triangle are positive integers, and the numerical value of its perimeter is equal to the numerical value of its area, then it is called a "standard right-angled triangle". Then, the number of standard right-angled triangles is ( ).
(A) 1
(B) 2
(C) 3
(D) infinitely many
3. B.

Let the three sides of a triangle be $a$, $b$, and $c$ (with $c$ being the hypotenuse). Then,
$$
\begin{array}{l}
a^{2}+b^{2}=c^{2}, a+b+c=\frac{a b}{2} \\
\Rightarrow a+b+\sqrt{a^{2}+b^{2}}=\frac{a b}{2} \\
\Rightarrow \frac{a^{2} b^{2}}{4}-a^{2} b-a b^{2}+2 a b=0 .
\end{array}
$$

Since $a$, $b$, and $c$ are all positive integers, we have,
$$
\frac{a b}{4}-a-b+2=0 \Rightarrow(a-4)(b-4)=8 \text {. }
$$

Thus, the pairs $(a, b, c)$ that satisfy the conditions are $(6,8,10)$ and $(5,12,13)$.
Therefore, there are 2 right-angled triangles that meet the conditions.