In trapezoid CDEF (CF || DE) through vertex E, a straight line EM is drawn parallel to side CD and intersecting

| September 16, 2021 | education

In trapezoid CDEF (CF || DE) through vertex E, a straight line EM is drawn parallel to side CD and intersecting side CF at point M. The perimeter of a triangle whose sides are the midlines of triangle EMF is 12 cm.Find the perimeter of the trapezoid if DE = 6 cm.

Consider the triangle ABK, built along the midlines of the triangle MEF. Since the middle line of the triangle is equal to half the length parallel to its side, the perimeter of the triangle MEF is twice the perimeter of ABK.

Рmef = 2 * 12 = 24 cm.

Since by condition CD is parallel to ME, their lengths are equal to CD = ME.

The perimeter of the trapezoid is:

P = CD + DE + EF + CF.

CF = (CM + MF) = (6 + MF).

CD = ME.

Then P = ME + DE + EF + CM + MF.

(ME + EF + MF) = 24, since this is the perimeter of triangle MEF.

P = DE + CM + Pmef = 6 +6 + 24 = 36 cm.



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