The sum of the areas of two circles is 8pie square meters. Find the length of a radius of each circle ifone of them is twice as long as the other.what is the radius of the larger circle?

The sum of the areas of two circles is 8pie square meters Find the length of a radius of each circle ifone of them is twice as long as the otherwhat is the radi class=

Respuesta :

nice

area=pir^2
the areas are
pir^2+pi(2r)^2
they add to 8pi

8pi=pir^2+pi(2r)^2
undistribute pi
8pi=pi(r^2+(2r)^2)
divide both sides by pi
8=r^2+(2r)^2
expand
8=r^2+4r^2
add
8=5r^2
divide by 5
8/5=r^2
sqrt both sides
√(8/5)=r
double since it is double
2√(8/5) is radius of bigger aka (4√10)/5

radius=(4√10)/5