One of the angles of the parallelogram is 150 degrees, and the diagonal is 6, perpendicular

| May 7, 2021 | education

One of the angles of the parallelogram is 150 degrees, and the diagonal is 6, perpendicular to the side. Find the perimeter of the parallelogram

Since the diagonal BD is perpendicular to the sides AD and BC, the triangles ABD and BCD are rectangular.

In a right-angled triangle ABD, the angle ABD = (180 – CBD) = (180 – 90) = 60, then the angle BAD = (90 – ABD) = (90 – 60) = 30.

Leg BD lies opposite angle 30, then its length is equal to half the length of the hypotenuse AB.

BD = AB / 2.

AB = 2 * BD = 2 * 6 = 12 cm.

By the Pythagorean theorem, AD ^ 2 = AB ^ 2 – BD ^ 2 = 144 – 36 = 108.

АD = 6 * √3 cm.

In a parallelogram, the lengths of the opposite sides are equal, then its perimeter is:

Ravsd = 2 * (AB + AD) = 2 * (12 + 6 * √3) = 12 * (2 + √3) cm.

Answer: The perimeter of the parallelogram is 12 * (2 + √3) cm.



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