Points DCE lie on the segment AB. Point D is the midpoint of segment AC, and longing E is the midpoint of segment CB.

Points DCE lie on the segment AB. Point D is the midpoint of segment AC, and longing E is the midpoint of segment CB. The distance between points D and E is 8 cm, find the length of the segment AB.

Let’s write the condition of the problem in letters:

AD = DC, CE = EB, DC + CE = 8 cm, AB =?.

In order to find the length of the segment AB, you need to find the sum of the smaller segments

AB = AD + DC + CE + EB = (AD + EB) + (DC + CE).

By the condition of the problem AD = DC, EB = CE,

let’s make the change (AD + EB) = (DC + CE),

AB = (DC + CE) + (DC + CE).

Substitute the value DC + CE = 8 cm,

AB = 8 cm + 8 cm = 16 cm.