Question

A line 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?

Answer 1

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

Answer 2

33

$\frac{x-7}{x} = \frac{2x-10}{2x+12}$ → x = $\frac{21}{2}$

AC = x + x + 12 = $\frac{21}{2} + \frac{21}{2}$ +12 = 33