Find the perimeter of a rhombus whose height is 8 cm and the obtuse angle is 5 times larger than the acute one.

Let the magnitude of the acute angle be equal to X0, then the magnitude of the obtuse angle of the rhombus is 5 * X0.

The sum of the adjacent corners of the rhombus is 180, then X + 5 * X = 180.

X = 180/6 = 30.

Angle BAD = 30.

Let’s build the height BH, then in the right-angled triangle ABH the leg BH lies opposite the angle 30, then the hypotenuse AB = 2 * BH = 2 * 8 = 16 cm.

Let’s define the perimeter of the rhombus.

Ravsd = 4 * AB = 4 * 16 = 64 cm.

Answer: The perimeter of the rhombus is 64 cm.