Answer: The length of MN is 6, length of NK is 4 and Length of MK is 5.
Explanation:
It is given that In △ABC, AB=8, BC=10, and AC=12. Let M, N, and K be the midpoints of the sides of △ABC.
The mid point theorem states that if a line segment joining the midpoints of two sides of the triangle, then the length of that line is half of the length of third line.
If M and N are mid points of AB and BC respectively, then the line MN must be parallel to AC and the length of MN is half of the length of AC.
[tex]MN=\frac{12}{2} =6[/tex]
If N and K are mid points of BC and AC respectively, then the NK line must be parallel to AB and the length of NK is half of the length of AB.
[tex]NK=\frac{8}{2} =4[/tex]
If M and K are mid points of AB and AC respectively, then the line MK must be parallel to BC and the length of MK is half of the length of BC.
[tex]MK=\frac{10}{2} =5[/tex]
Therefore, the length of MN is 6, length of NK is 4 and Length of MK is 5.
