Question

The perimeter of a △ABC equals 12 in. The midpoints of the sides M, N and K are connected consecutively. Find the perimeter of △MNK.

Answer 1

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,

$MN=\dfrac{1}{2}AC,\\ \\NK=\dfrac{1}{2}AB,\\ \\MK=\dfrac{1}{2}BC.$

The perimeter of the triangle MNK is

$P_{MNK}=MN+NK+MK=\dfrac{1}{2}AC+\dfrac{1}{2}AB+\dfrac{1}{2}BC=\dfrac{1}{2}(AC+AB+BC)=\dfrac{1}{2}P_{ABC}=\dfrac{1}{2}\cdot 12=6\ in.$