The bisector BM of triangle ABC divides side AC into segments AM and MC.

univerkov | June 12, 2021 | education

The bisector BM of triangle ABC divides side AC into segments AM and MC. Find the side length AC if AB = 10 cm, BC = 12 cm and AM = 8 cm.

We will use the property of the bisector of a triangle, according to which, the bisector divides the opposite side of the triangle into segments proportional to the adjacent sides.

Then AM / AB = CM / CB.

CM = AM * CB / AB = 8 * 12/10 = 9.6 cm.

Determine the length of the AC side. AC = AM + CM = 8 + 9.6 = 17.6 cm.

Answer: The length of the speaker side is 17.6 cm.

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