Two similar triangles have a ratio of corresponding sides of 3:7. If the smaller triangle has an area of 18, what is the area of the…

For similar figures, areas scale by the square of the ratio of sides. The ratio of the larger to the smaller is $\frac{7}{3}$, so the area ratio is $\frac{49}{9}$. The larger area is $18\cdot\frac{49}{9}=2\cdot49=98$, choice G. Choice F ($42$) multiplies by $\frac{7}{3}$ without squaring. Choice H ($126$) multiplies $18$ by $7$, using the side length as the scale factor. Choice J ($56$) does not correspond to any scale factor of $18$ that comes from a $3:7$ side ratio. When lengths scale by $k$, areas scale by $k^2$, and volumes scale by $k^3$.