Length of the Segment

On the side BC of triangle ABC, a point D is marked. The perimeter of triangle ABC is 15 centimeters, the perimeter of triangle ABD is 12 centimeters, and the perimeter of triangle ACD is 13 centimeters.
What is the length of segment AD?

Difficulty level (1 very easy - 10 very hard): 2

Geometry -> Plane Geometry -> Triangles Algebra -> Equations

Sources:

Young Mathematician Olympiad, 2020-2021, Stage A, Grades 7-8 Question 2

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