The bisector BD divides the side AC of triangle ABC into segments AD and CD

univerkov | August 10, 2021 | education

The bisector BD divides the side AC of triangle ABC into segments AD and CD, equal to 6 cm and 9 cm, respectively, AB = 8 cm. What is the perimeter of triangle ABC?

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 CD / CB = AD / AB.

CB = CD * AB / AD = 9 * 8/6 = 12 cm.

Determine the length of the AC side. AC = AD + CD = 6 + 9 = 15 cm.

Then the perimeter of the triangle is: Ravs = (AB + BC + AC) = 8 + 12 + 15 = 35 cm.

Answer: The perimeter of triangle ABC is 35 cm.

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