[Physics] the relationship between amplitude and the distance from the source of a water wave

Question

Attempt of the relation: Intensity $I \propto \frac{1}{r^2}$ and $I \propto A^2$.
So $A^2 \propto \frac{1}{r^2} \implies A \propto \frac{1}{r}$

Is it correct?

Answer 1

No, it's not correct. Think about why it is that $I \propto r^{-2}$ for (say) light or sound waves. There's something fundamentally different about water waves that changes this relationship.

Other than that, the rest of your logic is correct.