#### Answer

$x=0.5$ and $P=6$

#### Work Step by Step

Let us consider a configuration having $30-60-90$ angles (a triangle). The shorter leg of such a triangle is always half as long as the hypotenuse.
Here, hypotenuse $=1$
Thus, $x=(0.5) \times (1)=0.5$
Now, the perimeter of the hexagon is $P=12x$
This gives: $P=(12) (0.5)=6$
Hence, $x=0.5$ and $P=6$