The area of a circular ring located between 2 circles with a common center is 12 dm ^ 2

The area of a circular ring located between 2 circles with a common center is 12 dm ^ 2; the radius of the 1st circle is 2 times larger than the radius of the other, find these radii.

Let us express the radius of the smaller circle, for which we use the variable a.

Then the radius of the larger circle can be represented as 2a.

Consequently, the area in the first case can be written as an expression of πа ^ 2, while for a larger circle the value of the area will be expressed as 4πа ^ 2.

Since we know that their difference is 12 dm2, then we write down the equation and find out what the radii are equal to:

4πa ^ 2 – πa ^ 2. = 12;

3πa ^ 2 = 12;

a2 = 4 / π;

a1 = 2 / √π;

a2 = -2 / √π (not suitable).

2 * 2 / √π = 4 / √π.

Answer: 2 / √π dm and 4 / √π dm.