Question

the figures are similar. give the ratio of the perimeters and the ratio of the areas of the first figure to the second. the figures are not drawn to scale.
27 yd
24 yd
options:

• 9/8 and 11/10
• 10/9 and 81/64
• 10/9 and 11/10
• 9/8 and 81/64

Explanation:

Step1: Find the scale factor

The corresponding sides are 27 yd (first figure) and 24 yd (second figure). Scale factor $k = \frac{27}{24} = \frac{9}{8}$.

Step2: Ratio of perimeters

Perimeter ratio equals scale factor: $\frac{9}{8}$.

Step3: Ratio of areas

Area ratio equals square of scale factor: $(\frac{9}{8})^2 = \frac{81}{64}$.

Answer:

The ratio of perimeters is $\frac{9}{8}$ and the ratio of areas is $\frac{81}{64}$ (the last option in the image, assuming it's labeled correctly as the option with $\frac{9}{8}$ and $\frac{81}{64}$).