Question

If D is the midpoint of the segment AC and C is the midpoint of segment DB , what is the length of the segment AB , if AC = 3 cm.

Answer 1

Answer:  The length of segment AB is 4.5 cm.

Step-by-step explanation:  As shown in the attached figure, D is the mid-point of AC and C is the mid-point of DB. Also, AC = 3 cm.

We are to find the length of AB.

Since D is the mid-point of AC, so we have

AD : DC = 1 : 1,

and C is the mid-point of DB, so

DC : CB = 1 : 1.

Therefore, we can write

AD : DC : CB = 1 : 1 : 1.

From here, it implies that

$AC:CB=2:1\\\\\\\Rightarrow \dfrac{AC}{CB}=\dfrac{2}{1}\\\\\\\Rightarrow \dfrac{3}{CB}=2\\\\\\\Rightarrow CB=\dfrac{3}{2}\\\\\Rightarrow CB=1.5.$

Thus,

$AB=AC+CB=3+1.5=4.5.$

Hence, the length of segment AB is 4.5 cm.

Answer 2

Comment
The only way I can envision this is put all 4 points on 1 line segment. They go in the order of ADCB. I can only draw it this one way.

Given
D is the midpoint of AC
C is the midpoint of DB
AC = 3 cm

Argument
AC = 3 cm           Given
AD = DC                       D is the midpoint of AC
AD = 3/2                       Definition of a midpoint.
DC = 3/2                       Definition of a midpoint

DC = 3/2                       Last statement
DC + CB = 1.5 + 1.5.   C is the midpoint of BD
DB = 3                          Consolidation of equals
AD + DB = AB               
1.5 + 3 = 4.5                 Substitution.