Calculate the length of the bisector of angle A of triangle ABC with side lengths a = 18 cm, b = 15 cm, c = 12 cm.

univerkov | August 6, 2021 | education

By the property of the bisector of a triangle, the bisector of a triangle divides the third side into segments proportional to the other two sides, then AB / HB = AC / CH.

Let CH = X cm, then BH = (18 – X) cm.

12 / (18 – X) = 15 / X.

12 * X = 270 – 15 * X.

27 * X = 270.

X = 270/27 = 10 cm.

CH = 10 cm.

BH = 18 – 10 = 8 cm.

Then the length of the bisector is determined by the formula: AH = √ (AC * AB – CH * BH) = √ (15 * 12 – 10 * 8) = √100 = 10 cm.

Answer: The length of the bisector is 10 cm.

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