Final answer:
The length of segment AB is 4.5 cm since D is the midpoint of AC, and C is the midpoint of DB, with AC being 3 cm.
Step-by-step explanation:
To find the length of segment AB given that D is the midpoint of segment AC and C is the midpoint of segment DB, and that AC = 3 cm, we first consider the properties of midpoints. Since D is the midpoint of AC, we have AD = DC, and since AC = 3 cm, therefore AD = DC = 1.5 cm. Similarly, since C is the midpoint of DB, we have DC = CB, and therefore CB = 1.5 cm. To find AB, we add the lengths of AD, DC, and CB.
AB = AD + DC + CB
= 1.5 cm + 1.5 cm + 1.5 cm
= 4.5 cm
Thus, the length of segment AB is 4.5 cm.