The sides of the triangle are 4 cm, 6 cm, 8 cm. Find the perimeter of the triangle

| January 9, 2021 | education

The sides of the triangle are 4 cm, 6 cm, 8 cm. Find the perimeter of the triangle, the vertices of which are the midpoints of the sides of this triangle.

Let по ABC be given by hypothesis. Points M, N and K are the midpoints of sides AB, BC and AC, respectively. Thus, the sides of the new △ MNK are the midlines of the given one by the condition △ ABC, since they connect the midpoints of the sides of the triangle.
The perimeter of the triangle formed by the midlines of the triangle is half the perimeter of the original triangle.
Thus, the perimeter of △ MNK is equal to the perimeter of △ ABC divided by 2:
P △ MNK = P △ ABC / 2.
By assumption, the sides △ ABC are equal to AB = 4 cm, BC = 6 cm, AC = 8 cm.
Find the perimeter △ ABC:
P △ ABC = AB + BC + AC = 4 + 6 + 8 = 18 (cm).
The perimeter of △ MNK will be:
P △ MNK = 18/2 = 9 (cm).
Answer: P △ MNK = 9 cm.



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