Answer: The length of DC is 3 units
Step-by-step explanation:
The Basic proportionality theorem states that if a line is parallel to one side of a triangle and intersects the other two at different points, then the other two sides are divided in the same ratio.
The given image is attached below.
From the BPT theorem, we can say that:
[tex]\Rightarrow \frac{AE}{EB}=\frac{AD}{DC}[/tex]
We are given:
AE = 12 units
EB = 4 units
AD = 9 units
Putting values in above equation, we get:
[tex]\Rightarrow \frac{12}{4}=\frac{9}{DC}\\\\\Rightarrow DC=\frac{9\times 4}{12}\\\\\Rightarrow DC=3 units[/tex]
Hence, the length of DC is 3 units
