As always, the first step is to draw a picture.
Let $r$ be the radius of the circle. Then one side of the rectangle is equal to $2r$. And of course the opposite side has the same length.
From the tangency we can see that the other two sides are each equal to $r$.
(To prove this formally, let $O$ be the centre of the circle. Then the line that joins $O$ to the point $P$ of tangency has length $r$. This line is perpendicular to the long sides of the rectangle, and so has length equal to the short side of the rectangle. Thus the short sides of the rectangle have length $r$.)
So the perimeter of the rectangle is $6r$. The circumference of the circle is $2\pi r$. Since $\pi\gt 3$, the circumference is larger.
Remark: In this kind of problem, we can let the radius be $1$ (unit). That strategy can simplify formulas. In our case, there is no real gain.