From the statement of the problem, we know that the perimeter of the hexagon in the figure is:
[tex]P_{\text{hexagon}}=30.[/tex]
The perimeter is equal to the sum of the lengths of the sides. So each side of the hexagon has a length:
[tex]L_{\text{hexagon}}=\frac{30}{6}=5.[/tex]
The triangle inscribed in the hexagon is equilateral, so its three sides are equal. We see that the side AB of the triangle is also a side of the hexagon, so we have:
[tex]L_{\text{triangle}}=L_{\text{hexagon}}=5.[/tex]
The perimeter of the triangle is equal to the sum of the lengths of its sides, so:
[tex]P_{\text{triangle}}=3\cdot L_{\text{triangle}}=3\cdot5=15.[/tex]
Answer
The perimeter of △ABC is 15.
