[Equilateral Triangle]

Two equilateral triangles with perimeters of 12 and 15 are positioned such that their sides are respectively parallel (see Fig.1). Find the perimeter of the resulting hexagon.

#
Let $a, b, c, d, e$ and $f$ be the sides of the formed equilateral triangles (Fig.2). Then $b+a+f=15$ and $c+d+e=12$. Therefore, the perimeter of the hexagon is

$$
a+b+c+d+e+f=(a+b+f)+(c+d+e)=15+12=27
$$

## Answer

27.00