Find one of the diagonals of the rhombus, if the angle is 60 degrees, the perimeter is 16 cm.

univerkov | March 4, 2021 | education

Since the lengths of all sides of a rhombus are equal, the triangle ABD is equilateral, since AB = AD, and the angle A = 60, then BD = AB = AD.

Ravsd = 4 * AB, then AB = Ravsd / 4 = 16/4 = 4 cm.

Diagonal ВD = 4 cm.

AO is the height of an equilateral triangle AO = √3 * AB / 2 = 2 * √3 cm, then AC = 2 * AO = 4 * √3 cm.

Answer: The diagonals of the rhombus are 4 cm and 4 * √3 cm.

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