The bisector of angle A of parallelogram ABCD divides side BC into segments BK = 6cm

univerkov | February 1, 2021 | education

The bisector of angle A of parallelogram ABCD divides side BC into segments BK = 6cm and KC = 3cm. What is the perimeter of a parallelogram?

Since AK is the bisector of angle A, then the angle ВAK = DAK.

The sides of the BC and the AD are parallel, then the angles of the Ring Road and the ВKA are equal as they lie crosswise.

Then the angle ВAK = ВKA = DAK, and the triangle AВK is isosceles, AB = ВK = 4 cm.

BC side length = (ВK + СK) = 4 + 3 = 7 cm.

Then Ravsd = 2 * (AB + BC) = 2 * (4 + 7) = 22 cm.

Answer: The perimeter of the parallelogram is 22 cm.

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