Question

If the scale factor between two circles is 7a/9b what is the ratio of their areas?

Answer 1

. 49a2/81b2
I think the answer is B)

Answer 2

Answer:  The correct option is (B) $\dfrac{49a^2}{81b^2}.$

Step-by-step explanation:  Given that the scale factor between two circles is $\dfrac{7a}{9b}$.

We are to find the ratio of the areas of the two circles.

Let r and R be the radii of the two circles and A and B be the corresponding areas.

We know that the scale factor is the ratio of the radii of the two circles.

So, we have

$\dfrac{r}{R}=\dfrac{7a}{9b}\\\\\\\Rightarrow \dfrac{r^2}{R^2}=\dfrac{49a^2}{81b^2}\\\\\\\Rightarrow \dfrac{\pi r^2}{\pi R^2}=\dfrac{49a^2}{81b^2}\\\\\\\Rightarrow \dfrac{A}{B}=\dfrac{49a^2}{81b^2}.$

Thus, the required ratio of the areas of the two circles is $\dfrac{49a^2}{81b^2}.$

Option (B) is CORRECT.