Answer: x=2
Step-by-step explanation:
From the given picture, it can be seen that BE is parallel to CD in triangle ACD.
The basic proportionality theorem says that if a line(BE) is parallel to a side(CD) of a triangle(ACD) which intersects the other two sides (AC and AD) into two distinct points (B and E), then the line divides those sides in proportion.
Thus, we have [tex]\frac{AB}{BC}=\frac{AE}{ED}[/tex]
[tex]\frac{36}{12}=\frac{24}{6x-4}\\\\\Rightarrow6x-4=\frac{24\times12}{36}\\\\\Rightarrow6x-4=8\\\\\Rightarrow6x=12\\\\\Rightarrow x=2[/tex]
Hence, the value of x= 2
