Answer
$AF = s-a$
Work Step by Step
We can write an equation for each side of $\triangle ABC$:
$BD+CD = a$
$AE+CE = b$
$AF+BF = c$
Then:
$BD+CD + AE+CE + AF+BF = a+b+c$
$BD+CD + AF+CD + AF+BD = a+b+c$
$2BD+2CD + 2AF = a+b+c$
$BD+CD + AF = \frac{1}{2}(a+b+c)$
$BD+CD + AF = s$
$a + AF = s$
$AF = s-a$
