Similar scalene triangles are drawn on a coordinate plane. One triangle has side lengths of 3, 4, and 6. The other triangle has side lengths of 9 and 12, corresponding to the first triangle. Use the SSS criterion to determine the third side length of the corresponding triangle.(1 point)

To determine the third side length of the corresponding triangle based on the sides of the first triangle, we can use the concept of similarity of triangles.

The side lengths of the first triangle are 3, 4, and 6. The second triangle has sides of 9 and 12 that correspond to the sides of the first triangle.

Since the triangles are similar, the ratios of the sides must be the same.

Let's find the ratio of the corresponding sides:

- From the first triangle, one side (3) corresponds to the second triangle's side (9):
\[
\frac{9}{3} = 3
\]

- From the first triangle, another side (4) corresponds to the second triangle's side (12):
\[
\frac{12}{4} = 3
\]

Both of these ratios are equal to 3, confirming the triangles are similar.

Now we can find the third side length of the second triangle corresponding to the first triangle's side (6):

Using the similarity ratio:
\[
6 \times 3 = 18
\]

Thus, the length of the corresponding side of the second triangle is 18.

The correct response is \( \boxed{18} \).