Aline parallel to a triangle's side splits ab into lengths of x - 7 and x - 3. the other side, ac, is split into lengths of x and x + 12. what is the length of ac?

Given: x – 7 and x – 3 &  AC is split into lengths of x and x + 12.

Solution:

(x – 7) / (x – 3) = x / (x + 12)

(x – 7) (x + 12) = x (x – 3)

x^2 + 5x – 84 = x^2 -3x

8x = 84

x = 10.5
Thus,

AC = x + x + 12

= 10.5 + 10.5 + 12

= 33 would be the length of AC