The figures below are similar.
Figure 1: 28 yd Figure 2: 8 yd
What are a) the ratio of the perimeters and b) the ratio of the areas of the larger figure to the smaller figure? The figures are not drawn to scale.
A. 8/3 and 49/4
B. 7/2 and 49/4
C. 7/2 and 9/4
D. 8/3 and 9/4
Since the figures are similar, their corresponding side lengths are proportional. Let $x$ be the scale factor between the larger figure and the smaller figure (i.e. the ratio of their side lengths). Then, we have:
Figure 1: $28 = x \cdot s_1$
Figure 2: $8 = s_1$
where $s_1$ is the length of a side on the smaller figure. Solving for $x$ gives $x = \frac{28}{8} = \frac{7}{2}$.
a) The ratio of the perimeters is equal to the scale factor $x$, since all sides are scaled by the same factor. Therefore, the ratio of the perimeters is $\frac{7}{2}$.
b) The ratio of the areas is equal to the square of the scale factor, since both dimensions are scaled by $x$. Therefore, the ratio of the areas is $\left(\frac{7}{2}\right)^2 = \frac{49}{4}$.
Therefore, the answer is $\boxed{\textbf{(B)}\ 7/2 \text{ and } 49/4}$.