Find the set of numbers amongst the four options that is most like the given set $(49,25,9)$.

Let's look at the properties of the given set: $(49,25,9)$.
All the numbers in the set are perfect squares of consecutive decreasing odd numbers:

* $49=7^2$
* $25=5^2$
* $9=3^2$
The bases are consecutive odd numbers: $7,5,3$.

Now let's examine the options:

* Option A: $(39,26,13)$ – None of these numbers are perfect squares.
* Option B: $(36,25,16)=(6^2,5^2,4^2)$ – Squares of consecutive integers, both even and odd.
* Option C: $(64,27,8)=(8^2,3^3,2^3)$ – Mixture of squares and cubes.
* Option D: $(36,16,4)=(6^2,4^2,2^2)$ – All numbers are perfect squares of consecutive decreasing even numbers.

Option D matches the logic of being a sequence of squares of consecutive integers with a common difference of $2$ in their bases ($6,4,2$). Therefore, Option D is the most structurally similar set.