Given: triangle ABC, angle C-90 degrees, BC = 6 m, angle A = 30 degrees, MN, ME, NE- midlines.

Given: triangle ABC, angle C-90 degrees, BC = 6 m, angle A = 30 degrees, MN, ME, NE- midlines. find the perimeter of triangle MEN.

In a right-angled triangle ABC, the leg BC lies opposite the angle 30, then its length is half the length of the hypotenuse AB.

AB = 2 * BC = 2 * 6 = 12 cm.

By the Pythagorean theorem, we determine the length of the leg AC.

AC ^ 2 = AB ^ 2 – BC ^ 2 = 144 – 36 = 108.

AC = 6 * √3 m.

Segments МH, ME, HЕ are the middle lines of triangle ABC, then ME = AC / 2 = 6 * √3 / 2 = 3 * √3 m, MH = BC / 2 = 6/2 = 3 m, HE = AB / 2 = 12/2 = 6 m.

Then Rmen = 3 * √3 + 3 + 6 = 9 + 3 * √3 = 3 * (3 + √3) m.

Answer: The perimeter of the MEH triangle is 3 * (3 + √3) m.