SOLUTION: The sum of two areas of two circles is 128(pie)ft^2. The difference of the circumferences is 8(pie)ft. Find the radius of each circle.

Algebra ->  Equations -> SOLUTION: The sum of two areas of two circles is 128(pie)ft^2. The difference of the circumferences is 8(pie)ft. Find the radius of each circle.       Log On


   

Question 114401: The sum of two areas of two circles is 128(pie)ft^2. The difference of the circumferences is 8(pie)ft. Find the radius of each circle.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of two areas of two circles is 128(pie)ft^2. The difference of the circumferences is 8(pie)ft. Find the radius of each circle.
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Let the respective radii be "r" and "R"
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EQUATIONS:
(pi)r^2 + pi(R)^2 = 128pi
2pir - 2piR = 8pi
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Simplify:
r^2 + R^2 = 128
r - R = 4
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Substitute:
(R+4)^2 + R^2 = 128
2R^2 + 8R + 16 = 128
2R^2 + 8R - 112 = 0
R^2 + 4R - 56 = 0
R = [-4 +- sqrt(16-4*-56)]/2
R = [-4 +- sqrt(240)]/2
R = [-4 + sqrt(240)]/2 = 5.745966692...
r = 4+R = 9.745966692...
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Cheers,
Stan H.