Points D, C, E lie on the segment AB. Point D is the middle of the AC, point E is the middle of the CB

Points D, C, E lie on the segment AB. Point D is the middle of the AC, point E is the middle of the CB. The distance between D and E is 16 cm. Find the length AB

Let AD = x, CE = y. Then AC = AD + CD = 2AD = 2y, BC = CE + EB = 2CE = 2y.
DE = DC + CE = x + y.
According to the condition of the problem, the distance between D and E is 16 cm, that is, x + y = 16 cm.
We need to find the length of AB. AB = AC + CB = 2x + 2y.
Let’s compose the system: {AB = 2x + 2y; x + y = 16.
{AB = 2 (x + y); x + y = 16.
AB = 2 * 16 = 32 (cm).
Answer: 32 cm.