Answer:
Perimeter of ΔMNK is 6 in.
Step-by-step explanation:
Midpoint Theorem-
It states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.
M, N and K are the midpoints of the sides.
So,
- [tex]KN=\frac{1}{2}AB[/tex]
- [tex]NM=\frac{1}{2}CA[/tex]
- [tex]MK=\frac{1}{2}BC[/tex]
Perimeter of a ΔABC is 12 in, i.e [tex]AB+CA+BC=12[/tex] in
Perimeter of ΔMNK is,
[tex]=KN+NM+MK[/tex]
[tex]=\dfrac{1}{2}AB+\dfrac{1}{2}CA+\dfrac{1}{2}BC[/tex]
[tex]=\dfrac{1}{2}(AB+CA+BC)[/tex]
[tex]=\dfrac{1}{2}(12)[/tex]
[tex]=6[/tex] in
