The bisector AK of the angle BAD of the parallelogram ABCD divides the BC side into segments

univerkov | August 3, 2021 | education

The bisector AK of the angle BAD of the parallelogram ABCD divides the BC side into segments BK = 7 and KC = 5. Find the perimeter of this parallelogram.

Since AK is the bisector of the angle BAD, it forms an isosceles triangle at the lateral side AB, then BK = AB = 7 cm.

The length of the longer side of the parallelogram BC = ВK + СK = 7 + 5 = 12 cm.

By the property of a parallelogram, the lengths of its opposite sides are equal, then AB = CD = 7 cm, AD = BC = 12 cm.

The perimeter of the parallelogram ABCD is:

Ravsd = 2 * (AB + BC) = 2 * (7 + 12) = 38 cm.

Answer: The perimeter of the parallelogram is 38 cm.

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