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Question 233650: The perimeter of a semicircular region, measured in meters, is numerically equal to its area, measured in square meters. The radius of the semicircle, measured in meters, is
a) 2/pi b) ½ c) pi d) 1 e) 4/pi +2
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The perimeter of a semicircular region, measured in meters, is numerically equal to its area, measured in square meters. The radius of the semicircle, measured in meters, is
a) 2/pi b) ½ c) pi d) 1 e) 4/pi +2
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Perimeter = (1/2)2(pi)r + 2r = (pi)r + 2r = (2+(pi))r meters
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Area = (pi)r^2
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Equation:
(2+(pi))r = (pi)r^2
pi*r^2 - (2+pi)r = 0
r(pi*r - (2+pi)) = 0
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Non-zero solution:
r = (2+pi)/pi
r = (2/pi) = 1
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Cheers,
Stan H.
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