Answer:
56
Step-by-step explanation:
Let's say that D is the point where AB is split, so AD = x-6 and DB = x.
And let's say that E is the point where AC is split, so AE = x+6 and EC = x+20.
Triangle ADE is similar to triangle ABC. Therefore:
(x-6) / (x-6 + x) = (x+6) / (x+6 + x+20)
Solving:
(x-6) / (2x-6) = (x+6) / (2x+26)
(x-6) (2x+26) = (x+6) (2x-6)
2x² + 26x - 12x - 156 = 2x² - 6x + 12x - 36
2x² + 14x - 156 = 2x² + 6x - 36
14x - 156 = 6x - 36
8x = 120
x = 15
So the length of AC is:
AC = x+6 + x+20
AC = 2x + 26
AC = 2(15) + 26
AC = 56
