The corners of the rhombus have a ratio of 1: 2, and the smaller diagonal is 15 cm. What is the perimeter of the rhombus?

Let the acute angle of the rhombus be X0, then, by condition, the obtuse angle is 2 * X.

Since the opposite angles of a rhombus are equal, the sum of adjacent angles is 180, then:

X + 2 * X = 180.

3 * X = 180.

X = BAD = BCD = 180/3 = 60.

Then the obtuse angle is: ABC = ADC = 60 * 2 = 120.

In a rhombus, all sides are equal. Then in a triangle ABD, AB = AD, and the angle BAD = 60. If, in an isosceles triangle, one of the angles is 60, then such a triangle is equilateral.

AB = AD = BD = 15 cm.

Let’s define the perimeter of the rhombus.

Ravsd = AB + BC + CD + AD = 4 * 15 = 60 cm.

Answer: The perimeter of the rhombus is 60 cm.