A circular pond has radius r. The area of a pond whose radius is 6m more than r is 4 times the area of the first pond. The radius r of the first pond equals

Answer 1

A1 = pi*r^2

A2 = pi*(r+6)^2 = 4A1 = 4*pi*r^2
pi*(r+6)^2 = 4*pi*r^2
Divide both sides by pi:
(r+6)^2 = 4r^2
r^2 + 12r + 36 = 4r^2
r^2 - 4r^2 + 12r +36 = 0
-3r^2 + 12r + 36 = 0
Divide both sides by -3:
r^2 - 4r - 12 = 0
(r-6)(r+2) = 0

r-6 = 0
r = 6.

r+2 = 0
r = -2

Select positive value of r:
r = 6 m