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kolbaska11 [484]
3 years ago
12

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.

Mathematics
1 answer:
Zarrin [17]3 years ago
4 0

Answer:

<em>Perimeter of ΔMNK is </em><em>6 in.</em>

Step-by-step explanation:

<u>Midpoint Theorem-</u>

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

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