Answer: 25 units.
Step-by-step explanation:
Given: B is the midpoint of line segment AC.
[tex]\Rightarrow\ AB=\dfrac{AC}{2}[/tex]
If [tex]AB = 4x + 1[/tex] and [tex]AC = 5x + 20[/tex], then we have
[tex]4x+1=\dfrac{5x+20}{2}[/tex]
Multiply 2 on both sides, we get
[tex]2(4x+1)=5x+20\\\\\Rightarrow\ 8x+2=5x+20\\\\\Rightarrow\ 8x-5x=20-2\\\\\Rightarrow\ 3x=18\\\\\Rightarrow\ x= 6[/tex]
Now, AC = 5(6)+20 =30+20=50 units
Then, BC= [tex]\dfrac{50}{2}=25\text{ units}[/tex]
Hence, the length of BC is 25 units.
