sat-dog

The correct answer is $\frac{135}{8}$. It's given that triangles $\text{A}\text{B}\text{C}$ and $\text{D}\text{E}\text{F}$ are similar and each side length of triangle $\text{A}\text{B}\text{C}$ is $4$ times the corresponding side length of triangle $\text{D}\text{E}\text{F}$. For two similar triangles, if each side length of the first triangle is $k$ times the corresponding side length of the second triangle, then the area of the first triangle is $k^2$ times the area of the second triangle. Therefore, the area of triangle $\text{A}\text{B}\text{C}$ is $4^2$, or $16$, times the area of triangle $\text{D}\text{E}\text{F}$. It's given that the area of triangle $\text{A}\text{B}\text{C}$ is $270$ square inches. Let $a$ represent the area, in square inches, of triangle $\text{D}\text{E}\text{F}$. It follows that $270$ is $16$ times $a$, or $270=16a$. Dividing both sides of this equation by $16$ yields $\frac{270}{16}=a$, which is equivalent to $\frac{135}{8}=a$. Thus, the area, in square inches, of triangle $\text{D}\text{E}\text{F}$ is $\frac{135}{8}$. Note that 135/8, 16.87, and 16.88 are examples of ways to enter a correct answer.