Question

a line parallel to a triangle’s side splits line AB into lengths of x-6 and x. the other side, line AC, is split into lengths of x+6 and x+20. what is the length of AC ?

Answer 1

56

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