Answer
$\dfrac{3}{4}$ and $3: 4$
Work Step by Step
We can see that the ratio of the perimeters of two smaller figures is $\dfrac{a}{b}$, and the ratio of their areas is the square of the ratio of their perimeters:
$\dfrac{a^2}{b^2}$.
Set up a proportion:
$\dfrac{a^2}{b^2}=\dfrac{18}{32} \\ \dfrac{a}{b}=\sqrt {\dfrac{9}{16}}$
This implies that the square factor is $ \dfrac{a}{b}=\dfrac{3}{4}$
So, the ratio of the perimeters is equal to the scale factor, which is $ 3:4$.