To determine how many smaller right triangles with a side length of \(5\sqrt{3}\) cm can fit along the side length of a larger right triangle with a side length of \(40\sqrt{12}\) cm, we first need to simplify the side length of the larger triangle.
Starting with the side length of the larger triangle: \[ 40\sqrt{12} = 40\sqrt{4 \times 3} = 40 \times 2\sqrt{3} = 80\sqrt{3} \text{ cm} \]
Now, we want to find out how many smaller triangles of side length \(5\sqrt{3}\) cm can fit into \(80\sqrt{3}\) cm.
To find this, we divide the length of the larger triangle by the length of the smaller triangle: \[ \frac{80\sqrt{3}}{5\sqrt{3}} = \frac{80}{5} = 16 \]
Thus, \(16\) smaller right triangles of side length \(5\sqrt{3}\) cm can fit along the longer side length of the larger right triangle.
The answer is: \[ \boxed{16} \]