To determine how many smaller right triangles with side lengths of \(5\sqrt{3}\) centimeters fit along the larger right triangle's side length of \(40\sqrt{12}\) centimeters, we will first simplify the larger triangle's side length.
We know:
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
Thus, we can substitute this into the side length:
\[ 40\sqrt{12} = 40 \times 2\sqrt{3} = 80\sqrt{3} \text{ centimeters} \]
Now we want to find out how many smaller triangles with side length \(5\sqrt{3}\) can fit along this length of \(80\sqrt{3}\) centimeters. We calculate this by dividing the larger triangle's length by the smaller triangle's length:
\[ \text{Number of smaller triangles} = \frac{80\sqrt{3}}{5\sqrt{3}} \]
The \(\sqrt{3}\) in the numerator and denominator cancels out:
\[ = \frac{80}{5} = 16 \]
Therefore, the number of smaller lengths running along the longer length is
\[ \boxed{16} \]