Triangle annulus?

The area of the smaller triangle is $\dfrac{1}{2}(24)(32)-330=54$ . Let $x,y$ and $z$ be the side lengths of the smaller triangle. Then, $54=\dfrac{1}{2}xy$ or $xy=108$ . Since the two triangle are similar we have $\dfrac{x}{24}=\dfrac{y}{320}$ or $x=\dfrac{3}{4}y$ . By substitution we get, $\dfrac{3}{4}y(y)=108$ or $y=12$ . It follows that $x=\dfrac{3}{4}(12)=9$ . By pythagorean theorem, $z=\sqrt{12^2+9^2}=15$ . So the perimeter is $12+9+15=36$ .