Question 374088: The sum of the area s of two circles is 65pi square feet. The length of a radius of the larger circle is one foot less than twice the length of the radius of the smaller circle. Find the length of a radius of each circle.
Answer by rfadrogane(214)   (Show Source):
You can put this solution on YOUR website! The sum of the area s of two circles is 65pi square feet. The length of a radius of the larger circle is one foot less than twice the length of the radius of the smaller circle. Find the length of a radius of each circle.
Sol'n:
let R - radius of big circle
r - radius of small circle
A1+A2 = 65pi
R^2pi + r^2pi = 65pi, eliminating pi on both side
R^2 + r^2 = 65 ----(1)
R = 2r-1 -----(2)
substitute (2)into (1),
(2r-1)^2 + r^2 = 65
4r^2 - 4r + 1 r^2 = 65
5r^2 - 4r - 64 = 0, factor then equate to zero to find the value of r.
r = 4---acceptable
r = -3.2----absurd,
thus,
r = 4 ft. -----ans.
R = 2(4)-1 = 7 ft. -----ans.
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