You are given a parallelogram ABCD. BE-bisector of angle ADC, CD = 8, BC = 12 Find the perimeter of the parallelogram.

According to the properties of a parallelogram, its opposite sides are equal:

AB = CD = 8 cm;

BC = AD.

Since the bisector of the angle of the parallelogram cuts off the isosceles triangle from it, the segment EC is equal to the side CD:

EC = CD = 8 cm.

The perimeter of a parallelogram is the sum of the lengths of all its sides:

P = AB + BC + CD + AD.

Let’s find the length of BC and AD:

BC = AD = BE + EC;

BC = AD = 12 cm + 8 cm = 20 cm;

P = 20 cm + 8 cm + 20 cm + 8 cm = 56 cm.

Answer: The perimeter of this parallelogram is 56 centimeters.

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