In triangle ABC, AD is the bisector. Find the segments BD and DC, if AB = 14 cm, BC = 20 cm, AC = 21 cm.

univerkov | February 8, 2021 | education

Let the length of the segment ВD = X cm, then the length of the segment DС = (BC – X) = (20 – X) cm.

By the property of the bisector of a triangle, it divides the opposite side into segments proportional to the adjacent sides.

AВ / ВD = AC / DС.

14 / X = 21 / (20 – X).

21 * X = 280 – 14 * X.

35 * X = 280.

X = 280/35 = 8 cm.

ВD = 8 cm.

DС = 20 – 8 = 12 cm.

Answer: The length of the ВD segment is 8 cm, the length of the DС segment is 2 cm.

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