Two similar rectangular gardens have corresponding side lengths in the ratio 3:4. What is the ratio of their areas?

When two figures are similar, their areas are in the ratio of the squares of their corresponding lengths. The sides are in the ratio $3:4$, so the areas are in the ratio $3^2 : 4^2 = 9:16$, choice A. Check with numbers: gardens of 3 by 3 and 4 by 4 have areas 9 and 16. Choice B ($3:4$) is the ratio of lengths, not areas. Choice C ($6:8$) is just $3:4$ doubled, which simplifies to the same length ratio. Choice D ($12:16$) simplifies to $3:4$ as well. Only squaring the ratio accounts for both dimensions growing together.