In a triangle ABC, AB = 16cm, BC = 18cm, AC = 20cm. Find the lengths of the line segments by which the BC
| March 23, 2021 | education
In a triangle ABC, AB = 16cm, BC = 18cm, AC = 20cm. Find the lengths of the line segments by which the BC side is divided by this bisector of angle A.
Let the length of the segment BD = X cm, then the length of the segment CD = (CB – BD) = (18 – X) cm.
By the property of the bisector of the angle of a triangle, it divides the opposite side into segments proportional to the adjacent sides.
CD / AC = BD / AB.
(18 – X) / 20 = X / 16.
20 * X = 16 * (18 – X)
20 * X + 16 * X = 288.
40 * X = 288.
X = BD = 288/40 = 7.2 cm.
CD = 18 – 7.2 = 11.8 cm.
Answer: The bisector divides the BC side into 7.2 cm, 11.8 cm segments.
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