In rhombus ABCD, angle A is 60 degrees. Find: the perimeter of the rhombus if the diagonal ВD is 15 cm.

The diagonals of the rhombus divide the corners at the vertices in half, and form a right angle at the point of intersection. Then the angle BAC = BAD / 2 = 60/2 = 30, and the AВO triangle is rectangular.
The diagonals at the point of intersection are divided in half, then ВO = ВD / 2 = 15/2 = 7.5 cm.
In a right-angled triangle ABO, the ВO leg lies opposite the angle of 300, then the hypotenuse AB is equal to two lengths of the ВO leg.
AB = 2 * ВO = 2 * 7.5 = 15 cm.
Since all sides of a rhombus are equal, then Ravsd = 4 * AB = 4 * 15 = 60 cm.
Answer: The perimeter of the rhombus is 60 cm.