BD is the median of the isosceles triangle ABC with the base AC. Find BD if the perimeters of triangles

BD is the median of the isosceles triangle ABC with the base AC. Find BD if the perimeters of triangles ABC and ABD are 4.6 and 3.8 cm, respectively.

We will use the formula for the perimeter of a triangle and write down the perimeter for each of the two triangles, taking into account that the triangle ABC given by the condition is isosceles:
P ABC = AB + BC + AC = 2AB + AC = 4.6.
P ABD = AB + 0.5AC + BD = 3.8
We got a system of two linear equations:
2AB + AC = 4.6
AB + 0.5AC + BD = 3.8
For the solution we will use the addition method.
Multiply the second equation by (-2) and add both equations:
2AB + AC = 4.6
-2AB – AC – 2BD = -7.6
-2BD = – 3
BD = 1.5 (cm).
Answer: The median BD is 1.5 cm.