Find the length of the segment ND if CD is 34 cm, CM is 13 cm, and MN is 5 cm less than CM.

Let the points M and N be marked on the segment CD in such a way that the point M lies between the points C and N, and the length of the segment ND = x cm, then:

13 – 5 = 8 (cm) is the length of the segment MN, since it is known from the condition of the problem that the length of the segment CM is 13 cm, and MN is less than CM by 5 cm.

Knowing that the length of the segment CD is 34 cm and in accordance with the axioms of the relative position of points on the straight line and the relationship of the lengths of the obtained segments, we obtain the equality CD = CM + MN + ND and compose the equation:

13 + 8 + x = 34;

x = 13 (cm) – length of the segment ND.

Answer: The length of the ND segment is 13 cm.