The bisector BD divides the AC side of the ABC triangle into segments AD and CD, equal to 7cm and 10.5 cm, respectively.

univerkov | August 15, 2021 | education

The bisector BD divides the AC side of the ABC triangle into segments AD and CD, equal to 7cm and 10.5 cm, respectively. Find the perimeter of the ABC triangle, if known, then AB = 9cm.

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 AD / AB = CD / CB.

СВ = AB * CD / AD = 9 * 10.5 / 7 = 13.5 cm.

Determine the length of the AC side. AC = AD + CD = 7 + 10.5 = 17.5 cm.

Then the perimeter of the triangle is equal to: Ravs = (AB + BC + AC) = 9 + 13.5 + 17.5 = 40 cm.

Answer: The perimeter of triangle ABC is 40 cm.

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