Perimeter of the obtained star.

Here's a simple solution:

Let's call the side length of one of the two congruent triangles $s$ . When the two triangles are superimposed, a hexagon with 6 $\frac{s}{3}$ or 2 $s$ is made from the removed sides. So because there are two congruent triangles with side length $s$ , 6 $s$ -2 $s$ , or rather 4 $s$ would be the answer. The perimeter of one of the triangles is 54, so $s$ would be 4 $\frac{54}{3}$ , or $72$ .