1970 AHSME Problem 27

In a triangle, the area is numerically equal to the perimeter. What is the radius of the inscribed circle?

\textbf{(A) }2\qquad \textbf{(B) }3\qquad \textbf{(C) }4\qquad \textbf{(D) }5\qquad \textbf{(E) }6

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.