One of the corners of the rhombus = 120 °. find the smaller diagonal of the rhombus if its perimeter = 24cm.

Let us determine the length of the side of the indicated rhombus, knowing by the condition of the problem that its perimeter is 24 centimeters:

24: 4 = 6.

Let us determine the degree value of the angle that is formed by the smaller diagonal of the indicated rhombus and its side, knowing that, by definition, the diagonal divides the corners of the rhombus in half:

120: 2 = 60.

Determine how many centimeters the length of the smaller diagonal of this rhombus is equal to:

2 * (6 * cos 60 °) = 2 * 6 * 1/2 = 6.

Answer: The length of the smaller diagonal of the indicated rhombus is 6 centimeters.