Answer:
[tex]18+6\sqrt{3}[/tex]
Step-by-step explanation:
In all 30-60-90 triangles, the side lengths are in the ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]2x[/tex] is the length of the hypotenuse, or longest side, of the triangle and [tex]x[/tex] is the length of the side that is directly opposite to the 30 degree angle.
The figure consists of three 30-60-90 right triangles (two inside a larger one). The side KL is marked as 6 meters and represents the side opposite to the 30 degree angle of the largest triangle (Since [tex]\angle L=90^{\circ}[/tex] and [tex]\angle K=60^{\circ}[/tex]). Therefore, the hypotenuse (longest side) of the triangle must be [tex]2\cdot 6=12[/tex] and the other leg must be [tex]6\sqrt{3}[/tex].
The perimeter of a polygon is equal to the sum of all the polygon's sides and therefore the perimeter of thing triangle is [tex]6+12+6\sqrt{3}=\boxed{18+6\sqrt{3}}[/tex]
