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:

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,

1. $KN=\frac{1}{2}AB$
2. $NM=\frac{1}{2}CA$
3. $MK=\frac{1}{2}BC$

Perimeter of a ΔABC is 12 in, i.e $AB+CA+BC=12$ in

Perimeter of ΔMNK is,

$=KN+NM+MK$

$=\dfrac{1}{2}AB+\dfrac{1}{2}CA+\dfrac{1}{2}BC$

$=\dfrac{1}{2}(AB+CA+BC)$

$=\dfrac{1}{2}(12)$

$=6$ in