This problem involves the Triangle Midsegment Theorem, which states that a midsegment of a triangle is parallel to one side of the triangle and is half as long as that side.

Problem Analysis:

1. The triangle $\triangle LMN$ is formed by connecting the midpoints of the sides of $\triangle IJK$.
2. $LM$ is a midsegment of $\triangle IJK$, so it is parallel to $JK$ and is half its length.

Solution:

The length of $JK$ is given as $12$. By the Triangle Midsegment Theorem: $LM = \frac{1}{2} \cdot JK = \frac{1}{2} \cdot 12 = 6.$

Thus, the length of $LM$ is 6.

Would you like me to elaborate on the theorem or check anything else? Here are some follow-up questions you might find helpful:

Follow-up Questions:

1. How does the Triangle Midsegment Theorem relate to parallel sides in a triangle?
2. Can the midsegment property be used to determine the perimeter of $\triangle LMN$?
3. How do you verify that a segment is a midsegment in a triangle with coordinates?
4. What happens to the midsegment theorem in obtuse triangles?
5. Can we use the theorem to solve problems involving triangle similarity?

Tip:

Always ensure you identify the side of the triangle that the midsegment is parallel to before applying the midsegment theorem.