The area of two circles are in a ratio of 4:9. If both radii are integers, and r(1) - r(2) = 2, what is the radius of the larger circle?

Answer 1

The areas of two circles are proportional to the square of their raddi

so r1^2 / r2^2 = 9/4
r1/r2 = 3/2
r1 = 3r2/2

also r1 = r2 + 2
Thus:
3r2/2 = r2 + 2
3r2 = 2r2 + 4
r2 = 4
then r1 = 6

the larger radius is 6 units

check:
area of larger = 36π
area of smaller is 16π
ratio of larger : smaller = 36π : 16π = 36 : 16
= 9:4