The height of the rhombus equal to 3√3 divides its side into two equal parts. Find the perimeter of the rhombus.

Let the side of the rob be equal to 2 * X cm. AB = BC = CD = AD = 2 * X cm.

Then, by condition, the segment AH = DH = 2 * X / 2 = X cm.

The AВН triangle is rectangular, then, by the Pythagorean theorem:

BH ^ 2 = AB ^ 2 – AH ^ 2.

(3 * √3) ^ 2 = (2 * X) ^ 2 – X ^ 2.

27 = 4 * X ^ 2 – X ^ 2.

3 * X ^ 2 = 27.

X ^ 2 = 27/3 = 9.

X = 3.

Then AB = BC = CD = AD = 2 * 3 = 6 cm.

Let’s define the perimeter of the rhombus. Ravsd = 4 * 6 = 24 cm.

Answer: The perimeter of the rhombus is 24 cm.