An altitude drawn from the right angle of a right triangle divides the triangle into smaller, proportional triangles. First, we can use the Pythagorean theorem to find $A B$ : triangle $A D B$ is a Pythagorean triple in the ratio of $\(3-4-5\)$. In this case, the legs are 6 and 8 , so the hypotenuse will be 10 .
Since the triangles are proportional, their perimeters are proportional as well. The perimeter of triangle $\(A D B\)$ is $\(24(6+8+10)\)$, so we can set up the following equation, comparing the smallest sides of both triangles we're considering:

$$
\(\begin{aligned}
\frac{6}{10} & =\frac{24}{\text { Perimeter of } A B C} \\
6(\text { Perimeter of } A B C) & =240 \\
\text { Perimeter of } A B C & =40
\end{aligned}\)
$$