The bisector of an obtuse angle of a parallelogram divides the opposite side 8: 5 from the apex

univerkov | August 3, 2021 | education

The bisector of an obtuse angle of a parallelogram divides the opposite side 8: 5 from the apex of the acute angle. find the side if its pyrimeter is 84.

Let the length of the segment DМ = 5 * X cm, then, by condition, the length of the segment AM = 8 * X cm. The length of the side of HELL = (AM + DМ) = (8 * X + 5 * X) = 13 * X cm.

Since BM is the bisector of the angle ABC, the triangle ABM is isosceles, since the angle ABM = AMB. Then AB = AM = 8 * X cm.

By the property of the parallelogram BC = AD = 13 * X, AB = CD = 8 * X.

The perimeter of the parallelogram is: Ravsd = 2 * (AB + AD) = 2 * (8 * X + 13 * X) = 84.

42 * X = 84.

X = 84/42 = 2.

Then AB = CD = 2 * 8 = 16 cm.

Answer: The side is 16 cm.

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