One of the corners of the rhombus is 60 degrees. What is its perimeter if the length of the smaller diagonal of the rhombus is 20 cm?

The diagonals of the rhombus divide it into 4 right-angled triangles. Half of the smaller diagonal will be legs, 2 times less than the hypotenuse (because the opposite angles of the rhombus are 60 each, so 30 of them are half ==> legs are half of the hypotenuse.) the smaller diagonal of the rhombus is 20 cm, then its halves (legs) are equal to 10. To find the hypotenuse (side of the rhombus), you need 10 * 2 = 20. So all sides of the rhombus are equal, then the perimeter = 20 * 4 = 80cm.
Answer: 80cm