Find the perimeter of a rhombus if it is known that the smaller diagonal is 5 dm

| February 21, 2021 | education

Find the perimeter of a rhombus if it is known that the smaller diagonal is 5 dm, the angle between this diagonal and the side is 60 degrees.

A rhombus is called a four gon, in which all sides are equal, opposite angles are equal. The diagonals of the rhombus are perpendicular, that is, when they intersect, they form 4 right angles equal to 90 degrees, the diagonal of the rhombus divides the angle in half, at the point of intersection, the diagonal is divided in half.
Consider a rhombus AВСD and a triangle BOС formed by the side of the rhombus and half of two diagonals. The OВС angle is 60 degrees, the OВС angle = 90 degrees, the OВС angle = 180 – (90 + 60) = 30 degrees. The OВ side = 5/2 = 2.5 dm. The hypotenuse BC is the side of the rhombus and = 2.5 * 2 = 5 decimeters. The perimeter of the rhombus is 5 * 4 = 20 decimeters.
Answer: The perimeter of the rhombus is 20 decimeters.



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