The radius of one circle is 4 times longer than the radius of the second circle.

The radius of one circle is 4 times longer than the radius of the second circle. The sum of the areas of the circles is 51 cm2. How many centimeters is the radius of each circle?

Let us denote by x the radius of the smaller of the two given circles, expressed in centimeters.

In the initial data for this task, it is reported that the radius of the larger circle is four times the radius of the smaller one, therefore, the radius of the larger circle is 4x cm.

According to the condition of the problem, if we add up the areas of these two circles, then the result will be 51 cm², therefore, the following relationship holds:

πx² + π (4x) ² = 51,

We solve this equation:

πx² + 16πх² = 51;

17πх² = 51;

x² = 51 / (17π) = 3 / π;

x = √ (3 / π).

Therefore, the radius of the smaller circle is √ (3 / π) cm, and the radius of the larger circle is 4√ (3 / π) cm.

Answer: The radius of the smaller circle is √ (3 / π) cm, and the radius of the larger circle is 4√ (3 / π) cm.