9. One side of a triangle is 8, and the area is 12, then the minimum perimeter of this triangle is

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Answer 18.
Analysis As shown in the figure, in $\triangle ABC$, let $BC=8$, and the height from $A$ to $BC$ be $h$. Then, $S_{\triangle ABC}=\frac{1}{2} \times 8 \times h=12$, solving for $h$ gives $h=3$.
On one side of $BC$, construct a line $l \parallel BC$ and at a distance of 3 from $BC$. Reflect point $C$ over line $l$ to get point $C'$, and connect $BC'$, intersecting $l$ at $A'$. The perimeter of $\triangle A'BC$ is the smallest.
This is because $AB + AC = AB + AC' \geq BC' = BA' + A'C' = BA' + A'C$, at this point $A'B = A'C$.
Since $A'B^2 = BD^2 + A'D^2 = 4^2 + 3^2 = 25$, it follows that $A'C = A'B = 5$.
Therefore, the minimum perimeter of $\triangle ABC$ is $5 + 5 + 8 = 18$.