The bisector of angle A of parallelogram ABCD divides side BC into segments BK = 4 and KC = 3.

univerkov | June 30, 2021 | education

The bisector of angle A of parallelogram ABCD divides side BC into segments BK = 4 and KC = 3. The perimeter of the parallelogram is.

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

The sides ВС and АD are parallel, then the angles KAD and ВКА are equal as lying crosswise.

Then the angle BAC = BKA = DAK, and the triangle ABK is isosceles, AB = BK = 4 cm.

Side length BC = (BK + 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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