In a triangle with sides 6m, 8m and 10m, a bisector was drawn to the 8m side.

univerkov | September 29, 2021 | education

In a triangle with sides 6m, 8m and 10m, a bisector was drawn to the 8m side. Find the segments into which the bisector divides this side.

Let the length of the segment AM = X cm, then the length of the segment CM = (8 – X) cm.

To solve the problem, we apply the property of the bisector of the angle of a triangle, according to which it divides the opposite side of the triangle into segments proportional to the adjacent sides.

BC / CM = AB / AM.

10 / (8 – X) = 6 / X.

10 * X = 6 * (8 – X).

10 * X = 48 – 6 * X.

16 * X = 48.

X = AM = 48/16 = 3 cm.

Then CM = 8 – 3 = 5 cm.

Answer: The bisector divides the side into 5 cm and 3 cm segments.

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