In rhombus ABCD, angle A is 30 degrees. Perpendiculars BM and BK are drawn from vertex B to sides AD and CD, respectively. BM = 4cm. What is the perimeter of the rhombus.
Consider a right-angled triangle ABM, in which, by condition, the angle ABM = 30, the angle AMB = 90, since BM is perpendicular to AD. Then the BM leg lies opposite the angle 30 and, accordingly, is equal to half the length of the hypotenuse AB. ВM = AB / 2.
AB = 2 * BM = 2 * 4 = 8 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 * 8 = 32 cm.
Answer: The perimeter of the rhombus is 32 cm.
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