SOLUTION: Geometry. The perimeter of a semicircle is doubled when the radius is increased by 6. Find the radius of the semicircle.

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Question 630164:
Geometry. The perimeter of a semicircle is doubled when the radius is increased by 6. Find the radius of the semicircle.
Answer by dfrazzetto(283) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming a closed semicircle:
P = 2r + PI*r
2P = 2(r+6) + Pi(r+6)
2P = 2r + 12 + Pi*r + 6Pi
-2P = -4r - 2Pi*r
0 = -2r - Pi*r + 12 + 6Pi
2r + Pi*r = 12 + 6Pi
r(2+Pi) = 12 + 6Pi
r(2+Pi) = 6(2+Pi)
r = 6
Check
P = 12 + 6Pi
P(r+6) = 2(12) + Pi(12)
P = 24 + 12Pi = 2 (12 + 6Pi)