Find the perimeter of the triangle PQF if BC = 14 cm, AC = 16 cm, AB = 10 cm.

univerkov | April 30, 2021 | education

Points K, M, H are the midpoints of the sides BC, AB and AC of the triangle ABC, then the segments KN, KM, MN are the midlines of the triangle ABC.

Then KM = AC / 2 = 16/2 = 8 cm, KN = AB / 2 = 10/2 = 5 cm, MH = BC / 2 = 14/2 = 7 cm.

Points P, Q, F are the midpoints of the sides КМ, КН and МН of the triangle КМН, then the segments PQ, PF, QF are its midlines.

Then PQ = MH / 2 = 7/2 = 3.5 cm, QF = KM / 2 = 8/2 = 4 cm, PF = KH / 2 = 5/2 = 2.5 cm.

Ppqf = 3.5 + 4 + 2.5 = 10 cm.

Answer: The perimeter of the triangle PQF is 10 cm.

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