SOLUTION: The perimeter of a semicircle is doubled when the radius is increased by 0.5. Find the radius of the semicircle.

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Question 491907: The perimeter of a semicircle is doubled when the radius is increased by 0.5. Find the radius of the semicircle.
Found 2 solutions by ccs2011, richard1234:
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter of semi-circle is half the circumference.
--> %281%2F2%29%2A2%2Api%2Ar+=+pi%2Ar
If you double that it equals pi%28r%2B0.5%29
--> 2%2Api%2Ar+=+pi%28r%2B0.5%29
Solve for r
--> 2%2Api%2Ar+=+pi%2Ar%2B0.5pi
-->pi%2Ar+=+0.5pi
--> r+=+0.5
The radius is 0.5
Another way of looking at it is the perimeter is pi%2Ar, and pi is constant so the only way to double the perimeter is to double the radius
--> 2r = r + 0.5
--> r = 0.5

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter is a function of the radius, so if the perimeter is doubled then the radius is doubled. Hence the original radius is 0.5, because if it is increased by 0.5, the radius is doubled.