two rectangles. 1 is 28 cm. and other is 32 cm. the rectangles are similar.

When two rectangles are similar, the ratios of their corresponding side lengths, perimeters, and areas can be determined based on the ratios of their corresponding sides.

Given that the lengths of the similar rectangles are 28 cm and 32 cm, we can find the ratios as follows:

1. **Ratio of Side Lengths**:
To find the ratio of the side lengths, we can take the lengths of the two rectangles.
\[
\text{Ratio of side lengths} = \frac{28}{32} = \frac{7}{8}
\]

2. **Ratio of Perimeters**:
The perimeter of similar shapes is in the same ratio as their corresponding side lengths. Therefore, the ratio of the perimeters will also be the same.
\[
\text{Ratio of perimeters} = \frac{28}{32} = \frac{7}{8}
\]

3. **Ratio of Areas**:
The ratio of the areas of similar shapes is the square of the ratio of their corresponding side lengths.
\[
\text{Ratio of areas} = \left(\frac{28}{32}\right)^2 = \left(\frac{7}{8}\right)^2 = \frac{49}{64}
\]

Putting everything together, we have:

1. Ratio of side lengths: \(\frac{7}{8}\)
2. Ratio of perimeters: \(\frac{7}{8}\)
3. Ratio of areas: \(\frac{49}{64}\)