20.47 In a triangle, the area and its perimeter are numerically equal, the radius of its inscribed circle is
(A) 2.
(B) 3.
(C) 4.
(D) 5.
(E) 6.
[Solution] Let the inradius of $\triangle A B C$ be $r$ (as shown in the figure), then
$$
\begin{array}{c}
S_{\triangle A B C}=\frac{1}{2} \cdot A B \cdot r+\frac{1}{2} \cdot B C \cdot r+\frac{1}{2} \cdot A C \cdot r \\
=\frac{1}{2}(A B+B C+A C) r,
\end{array}
$$

If we set $p=A B+B C+A C$, from the given and the above equation, we have
$$
\begin{aligned}
& p=\frac{1}{2} p r, \\
\therefore \quad r & =2 .
\end{aligned}
$$

Therefore, the answer is $(A)$.