In the parallelogram ABCD, the perimeter is 34 cm. The angle C = 30, and the perpendicular

| August 22, 2021 | education

In the parallelogram ABCD, the perimeter is 34 cm. The angle C = 30, and the perpendicular to the straight line CD is 3 cm. Find the angles and sides of the parallelogram.

Consider a right-angled triangle ВСН, in which the angle H is straight, and the angle C = 30. Then the leg ВН lies opposite the angle 30 and is equal to half the length of the hypotenuse BC.

ВС = 2 * ВН = 2 * 3 = 6 cm.

Since the opposite sides of the parallelogram are equal, then AD = BC = 6 cm.

Knowing the perimeter and one of the sides, we determine the length of the other side.

AB = CD = (P – 2 * AD) / 2 = (34 – 2 * 6) / 2 = 11 cm.

In a parallelogram, opposite angles are equal, and the sum of adjacent angles is 180. Then Angle BAC = BCD = 30, ABC = ADC = 180 – 30 = 150.

Answer: The angles of the parallelogram are 30 and 150, the sides are 6 cm and 11 cm.



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