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

6 in

Explanation:

Because of the triangle midpoint therom

Answer 2

6 inches

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=(1)/(2)AC,\\ \\NK=(1)/(2)AB,\\ \\MK=(1)/(2)BC.`

The perimeter of the triangle MNK is

`P_(MNK)=MN+NK+MK=(1)/(2)AC+(1)/(2)AB+(1)/(2)BC=(1)/(2)(AC+AB+BC)=(1)/(2)P_(ABC)=(1)/(2)\cdot 12=6\ in.`