The sum of the areas of two circles is 80 square meters. Find the length of a radius of each circle if one of them is twice as long as the other.

Let the radius of the smaller circle be r, then the radius of the larger circle is 2r.

The area of a circle is given by the formula A = πr^2.

The sum of the areas of the two circles is 80 square meters:

πr^2 + π(2r)^2 = 80
πr^2 + 4πr^2 = 80
5πr^2 = 80
r^2 = 16
r = 4

The radius of the larger circle (2r) would be:
2r = 2(4) = 8

Therefore, the radius of the larger circle is 8 meters.