The smaller diagonal of the rhombus is 10 cm and the obtuse angle of the rhombus is 120 degrees.

The smaller diagonal of the rhombus is 10 cm and the obtuse angle of the rhombus is 120 degrees. Find the perimeter of the rhombus.

The diagonals of the rhombus divide it into 4 equal right-angled triangles.

The diagonals are halved by the intersection point, and the corners of the rhombus, from the vertex of which emanate, are halved.

Consider one of the triangles.

One of the legs will be 10: 2 = 5 cm.

The angle adjacent to the leg will be 120 °: 2 = 60 °.

The side of the rhombus is the hypotenuse of a right triangle.

cos 60 ° = 5 / a;

a = 5 / cos 60 °;

a = 10 cm.

The perimeter of a rhombus is the product of the side length of a rhombus and four:

P = 4 * a = 40 cm.