CD-midline of triangle AMN. Find the perimeter of triangle CDN if the perimeter of triangle AMN is 36 cm.

Since the middle line of this triangle connects the midpoints of the lateral sides, it is equal to half their length:
CN = AN / 2;

ND = NM / 2.

Its length is equal to half the length of the side to which it is parallel:

CD = AM / 2.

Based on this, we see that the sum of the lengths of all sides of the triangle ΔСND is equal to half of the perimeter of the triangle ΔANM:

PΔCND = P ΔANM / 2;

РΔСND = 36/2 = 18 cm.

Answer: the sum of all sides of the smaller triangle is 18 cm.