MN is the midline triangle ABC. Find the perimeter of the trapezoid AMNC if AB = 10cm, BC = 12cm, AC = 14cm.

The middle line of a triangle connects the midpoints of its two sides, is parallel to the third side and is equal to half its length.

MN – the middle line connecting the midpoints of the sides AB and BC of the triangle ABC and equal to half of the side AC of this triangle.

Hence, AM = BM = AB / 2 = 10/2 = 5 cm;

NC = BN = BC / 2 = 12/2 = 6 cm;

MN = AC / 2 = 14/2 = 7 cm.

The perimeter of the trapezoid AMNC is: PAMNC = AM + MN + NC + AC = 5 + 7 + 6 + 14 = 32 cm.