Question

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

Answer 1

By using the SSS criterion, we can see that the ratio of corresponding side lengths of the two triangles is the same. Therefore, if the second triangle has side lengths of $3$ and $12$, corresponding to the first triangle, then the third side length of the second triangle must be $6 \cdot \frac{12}{4} = \boxed{18}$.