The triangle proportionality theorem states that if a line parallel to a side of the triangle intersects the triangle, then the two sides are divided proportionally.
See the attached image. In [tex] \triangle {ABC} [/tex], [tex] \frac{AD}{DB} =\frac{AE}{EC} [/tex] according to the theorem stated above.
Let's create ratios to solve for x in this problem.
[tex] \frac{12}{9}=\frac{2x}{x+4} [/tex]
- Cross multiply (12 * x + 4) = (9 * 2x).
12x + 48 = 18x
- Subtract 12x from both sides.
48 = 6x
x = 8
