Question

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Answer 1

Given:

The scale factor between two circles is $\dfrac{2x}{5y}$.

To find:

The ratio of their areas.

Solution:

We know that, all circles are similar.

The ratio of the areas of similar figures is equal to the ratio of squares of their corresponding sides or equal to the square of ratio of their corresponding sides.

The scale factor is the ratio of the corresponding sides.

Ratio of areas of circles = Square of scale factor between two circles

$\text{Ratio of areas of circles}=\left(\dfrac{2x}{5y}\right)^2$

$\text{Ratio of areas of circles}=\dfrac{(2x)^2}{(5y)^2}$

$\text{Ratio of areas of circles}=\dfrac{4x^2}{25y^2}$

Therefore, the correct option is D.