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What is the ratio of the area of sector ABC to the area of sector DBE?
I am not quite sure how to do this. So far, since there are variables instead of numbers, I have got (pi)(r)^2:(pi)(3r)^2, but I know that is definitely wrong.

What is the ratio of the area of sector ABC to the area of sector DBE I am not quite sure how to do this So far since there are variables instead of numbers I h class=

Respuesta :

[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}\qquad \begin{cases} \theta =\textit{angle in degrees}\\ r=radius \end{cases}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{\triangleleft ABC}{\triangleleft DBE}\qquad \cfrac{\frac{\beta \pi (2r)^2}{360}}{\frac{3\beta \pi (r)^2}{360}}\implies \cfrac{\beta \pi (2r)^2}{360}\cdot \cfrac{360}{3\beta \pi (r)^2}\implies \cfrac{\beta \pi 2^2r^2}{360}\cdot \cfrac{360}{3\beta \pi r^2} \\\\\\ \cfrac{\beta \pi 4r^2}{3\beta \pi r^2}\implies \cfrac{4}{3}[/tex]

Answer:

4/3

Step-by-step explanation:


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