In a square, the diagonal divides the square into two congruent right-angled triangles. The length of the diagonal (\(d\)) can be found using the Pythagorean theorem in one of these triangles.

Given that the area of the square is 144 sq cm, we can find the length of one side (\(s\)) of the square by taking the square root of the area:

\[s^2 = 144\]

\[s = \sqrt{144} = 12\]

Now, in the right-angled triangle formed by half of the diagonal, one side (\(s\)) is the hypotenuse, and the other side is one of the legs. The length of the diagonal (\(d\)) is the hypotenuse.

Using the Pythagorean theorem:

\[d^2 = s^2 + s^2 = 2s^2\]

\[d = \sqrt{2s^2} = \sqrt{2} \cdot s = \sqrt{2} \cdot 12 = 12\sqrt{2} \, \text{cm}\]

So, the length of the diagonal of the square is \(12\sqrt{2}\) cm.

The correct answer is:

C. \(12\sqrt{2}\, \text{cm}\)