Respuesta :
Answer: The required similarity ratio is 1 : 10.
Step-by-step explanation: We are given to find the similarity ratio for the two circle with areas as follows:
[tex]A_1=2\pi~\textup{m}^2,\\\\A_2=200\pi~\textup{m}^2.[/tex]
Finding a similarity ratio for two circles is equivalent to finding the ratios of their radii.
Let, [tex]r_1[/tex] and [tex]r_2[/tex] be the radii of the two circles with areas [tex]A_1[/tex] and [tex]A_2[/tex] respectively.
So, we have
[tex]\dfrac{A_1}{A_2}=\dfrac{2\pi}{200\pi}\\\\\\\Rightarrow \dfrac{2\pi r_1^2}{2\pi r_2^2}=\dfrac{1}{100}\\\\\\\Rightarrow \dfrac{r_1^2}{r_2^2}=\dfrac{1}{100}\\\\\\\Rightarrow \dfrac{r_1}{r_2}=\dfrac{1}{10}~~~~~\textup{[taking square root on both sides]}\\\\\\\Rightarrow r_1:r_2=1:10.[/tex]
Thus, the required similarity ratio is 1 : 10.
