The bisector BK is drawn in parallelogram ABCD from the vertex of an obtuse angle B. Find the perimeter

univerkov | January 2, 2021 | education

The bisector BK is drawn in parallelogram ABCD from the vertex of an obtuse angle B. Find the perimeter of the parallelogram if AK: KD = 2: 1 and BC = 21.

Let the length of the segment DK = X cm, then, by condition, AK = 2 * X cm.
Since the opposite sides of the parallelogram are equal, then AD = BC = 21 cm.
AD = 21 = AK + DK = 2 * X + X.
3 * X = 21.
X = DK = 21/3 = 7 cm.
AK = 2 * 7 = 14 cm.
Since VK is the bisector of angle B, it cuts off the isosceles triangle ABK from the parallelogram. AB = AK = 14 cm.
Then the perimeter of the parallelogram is: Ravsd = 2 * (AB + AD) = 2 * (14 + 21) = 70 cm.
Answer: The perimeter of the parallelogram is 70 cm.

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