Given a triangle ABC, find its perimeter if the lengths of its midlines are 5.4 and 7.

Since the length of the middle line of the triangle is equal to half the length of the side parallel to it, then AC = 2 * KH = 2 * 7 = 14 cm, BC = 2 * KM = 2 * 4 = 8 cm, AB = 2 * MH = 2 * 5 = 10 cm.

Then Ravs = AC + BC + AB = 14 + 8 + 10 = 32 cm.

Second way.

Let’s define the perimeter of the triangle KMН.

Ркмн = КН + НМ + КМ = 7 + 5 + 4 = 16 cm.

Since KM, НM and KM are the middle lines, the KНM triangle is similar to ABC in three proportional sides with a similarity coefficient K = 1/2.

The perimeters of such triangles are referred to as the coefficient of their similarity.

Rknm / Ravs = 1/2.

Ravs = 2 * Rknm = 2 * 16 = 32 cm.

Answer: The perimeter of triangle ABC is 32 cm.