This answer is going to assume that the short side of the rectange is equal to the radius of the large circle.

Our goal is to find the short side of the rectangle. The short side must be between 6 and 12(radius and diameter of small circle). Let's start by finding some factor pairs for 243.

Pair 1: 1*243 (doesn't work)

Pair 2: 3*81(doesn't work)

Pair 3: 9*27(works)

As those are the only three pairs, pair 3 will work.

Now that we know the short side is 9, we can see that the radius of the large circle is **9**