Explanation:
the perimeter is the sum of all sides.
it is clearly a symmetric figure.
I assume the sqrt(36) is the whole baseline (incl. the left and right x).
so, we have
sqrt(8) + 2x = sqrt(36) = 6
1/2 × sqrt(8) + x = 3
sqrt(1/4 × 8) + x = 3
sqrt(2) + x = 3
x = 3 - sqrt(2)
to get the inclined sides we use Pythagoras
c² = a² + b²
c being the Hypotenuse, a and b being the legs of the right-angled triangle.
so,
side² = sqrt(8)² + (3 - sqrt(2))² = 8 + (9 - 6×sqrt(2) + 2) =
= 19 - 6×sqrt(2)
each inclined side is
sqrt(19 - 6×sqrt(2))
so, as perimeter we get
6 + sqrt(8) + 2×sqrt(19 - 6×sqrt(2)) =
= 15.3137085...