The diagonal of the rhombus is 10 cm and makes an angle of 60 ° with the side of the rhombus. Find the perimeter of the rhombus.

Draw a rhombus ABCD.
We draw one of the diagonals, for example, BD. Mark the angle between the diagonal and the side:
angle DBC = angle BDC = 60 degrees.
Consider a triangle BCD. He knows 2 angles, so you can find the third one:
BCD angle = 180 – (CBD angle + BDC angle) = 180 – (60 + 60) = 60 degrees. So the triangle is equilateral, and BC = CD = BD = 10 cm.
The perimeter of the rhombus ABCD = 4 * a, where a is the side length.
So the perimeter of ABCD = 4 * 10 = 40 cm