Answer:
6 inches
Step-by-step explanation:
Triangle midline theorem: In a triangle, the midline joining the midpoints of two sides is parallel to the third side and half as long.
Points M, N and K are midpoints of the sides AB, BC and AC. Acording to the Triangle midline theorem,
[tex]MN=\dfrac{1}{2}AC,\\ \\NK=\dfrac{1}{2}AB,\\ \\MK=\dfrac{1}{2}BC.[/tex]
The perimeter of the triangle MNK is
[tex]P_{MNK}=MN+NK+MK=\dfrac{1}{2}AC+\dfrac{1}{2}AB+\dfrac{1}{2}BC=\dfrac{1}{2}(AC+AB+BC)=\dfrac{1}{2}P_{ABC}=\dfrac{1}{2}\cdot 12=6\ in.[/tex]
