In rhombus ABCD, angle A is 30 °. From vertex B to sides AD and CD, perpendiculars BM and BK

In rhombus ABCD, angle A is 30 °. From vertex B to sides AD and CD, perpendiculars BM and BK are drawn, respectively, BM is 5 cm. What is the perimeter?

Consider a right-angled triangle ABM, in which, according to the condition, the angle ABM = 30, the angle AMB = 90, since the BM is perpendicular to the blood pressure. Then the BM leg lies opposite an angle of 30 and, accordingly, is equal to half the length of the AB hypotenuse. BM = AB / 2.

AB = 2 * BM = 2 * 5 = 10 cm.

In a rhombus, all sides are equal to each other, then the perimeter of the rhombus will be equal to: Ravsd = 4 * AB = 4 * 10 = 40 cm.

Answer: The perimeter of the rhombus is 40 cm.