Question

△abc and △def are similar. find the missing side length.
(the triangles are not drawn to scale.)

Explanation:

Step1: Find similarity ratio

$\text{Ratio} = \frac{AB}{DE} = \frac{8}{2} = 4$

Step2: Relate sides with ratio

Let the missing side be $x$ (side $DF$ corresponds to $AC$). So $\frac{AC}{DF} = 4$

Step3: Solve for missing side

$\frac{12}{x} = 4 \implies x = \frac{12}{4} = 3$

Answer:

3