2. (10 points) In triangle $A B C$, medians $A M$ and $B K$ are drawn. It is known that $A M=3, B K=5$. Determine which of the following statements is true:
a) the length of side $A B$ can be 6;

b) the perimeter of triangle $A B C$ can be 22;

c) based on the given data, it is impossible to estimate either the perimeter of the triangle or side $A B$

a) none of the listed answers are correct.

Select the correct answer, no need to provide a solution.
Answer: g).

Solution. Let $O$ be the point of intersection of the medians. As is known, the medians intersect in the ratio $2: 1$, counting from the vertex, so $B O=10 / 3$, $O K=5 / 3$, $A O=2$, $O M=1$. Let's now analyze the statements formulated in the problem.

Case a). We will use the triangle inequality for $A O B: A B<A O+$ $+O B=16 / 3<6$. Therefore, the statement of this item is incorrect.

Case b). Here, to estimate the perimeter, we will use the triangle inequality for $B O M$ and $A O K$:

$$
A B+B C+C A=A B+2 B M+2 A K<\frac{16}{3}+2 \cdot \frac{11}{3}+2 \cdot \frac{13}{3}=21 \frac{1}{3}<22
$$

Therefore, the statement of this item is also incorrect.

Case c). Using the triangle inequality, we can obtain upper estimates for both the side $A B$ and the perimeter. The statement is incorrect.

From this, we conclude that the statement of item g) is true.