The length of AB is 78.
Given,
C bisects AB.
If AC = 8x - 1 and BC = 4x + 19.
We need to find the length of AB.
We have,
C bisects AB.
It means AB into two equal halves.
So,
A________C________B
AC = BC
AC = 8x - 1 and BC = 4x + 19
8x - 1 = 4x + 19
Subtracting -4x on both sides
8x - 1 - 4x = 4x + 19 - 4x
4x - 1 = 19
Adding 1 on both sides
4x - 1 + 1 = 19 + 1
4x = 20
x = 20/4
x = 5
AB = AC + BC
AB = 8x - 1 + 4x + 19
AB = 12x + 18
AB = 12 x 5 + 18
AB = 60 + 18
AB = 78
Thus the length of AB is 78.
Learn more about bisecting a line and finding its length here:
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