Answer:
BC = 22
Step-by-step explanation:
B is the midpoint of AC:
This means that:
AC = AB + BC
Since B is the midpoint, we also have that the segments AB and BC are equal, then BC = AB
So
AC = AB + BC
AC = AB + AB
AC = 2AB
We have that:
AC = 8x - 20
AB = 2x + 6
So:
AC = 2AB
8x - 20 = 2(2x + 6)
8x - 20 = 2*2x + 2*6
8x - 20 = 4x + 12
8x - 4x = 12 + 20
4x = 32
x = 8
Now, we have that BC = AB, and AB = 2x + 6. So
BC = AB = 2x + 6
Since x = 8
2x + 6 = 2*8 + 6 = 12 + 6 = 22
BC = 22
