You are given a parallelogram ABCD. BE-bisector of angle ADC, CD = 8, BC = 12 Find the perimeter of the parallelogram.
May 28, 2021 | education
| 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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