Answer:
[tex]\displaystyle x=\frac{64}{3}[/tex]
Step-by-step explanation:
Similar triangles
If two triangles have the same internal angles the AAA theorem of similarity is met, thus the triangles are similar.
The lengths of the sides of similar triangles are proportional.
To find x, we relate the heights of the triangles with their bases. Thus,
[tex]\displaystyle \frac{32}{x}=\frac{12+6}{12}[/tex]
[tex]\displaystyle \frac{32}{x}=\frac{18}{12}[/tex]
Solving for x:
[tex]\displaystyle x=\frac{32*12}{18}[/tex]
Simplifying:
[tex]\displaystyle x=\frac{64}{3}[/tex]
