Answer:
The length of AC would be 168.
Step-by-step explanation:
A midpoint of the line segment is the point that is halfway between the endpoints of the line segment.
Since B is the midpoint of AC, we have AB=BC
here, [tex]AB=5\cdot x+9[/tex] and [tex]BC=8\cdot x-36[/tex]
AC=AB+BC
AC=BC+BC
[tex]AC=2\cdot BC[/tex]
∴[tex]AC=2(8x-36)=16x-72[/tex] ....(1)
to find the length of AC we have to find the value of x from the given condition i.e, AB=BC
[tex]5x+9=8x-36[/tex]
Combine like terms:
[tex]9+36=8x-5x[/tex]
[tex]45=3x[/tex]
∴[tex]x=15[/tex]
Now, putting the value of x in (1) we get,
AC[tex]=16x-72[/tex]
[tex]AC=16\cdot 15 -72[/tex]=[tex]240-72[/tex]=168
Therefore, the length of AC is 168.
