SOLUTION: The number of centimeters in the perimeter of semicircle is numerically the same as the number of square centimeters in its area. What is the number of centimeters in the radius

Algebra ->  Circles -> SOLUTION: The number of centimeters in the perimeter of semicircle is numerically the same as the number of square centimeters in its area. What is the number of centimeters in the radius      Log On


   

Question 333037: The number of centimeters in the perimeter of semicircle is numerically the
same as the number of square centimeters in its area. What is the number of
centimeters in the radius of the semicircle?
Found 2 solutions by jrfrunner, vksarvepalli:
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
Let P =the perimeter of semicircle
--
P = Circumference/2 + Diameter
P+=+%282%2Api%2Ar%29%2F2+%2B+2%2Ar
P+=+pi%2Ar+%2B2%2Ar
P+=+r%2A%28pi+%2B2%29
--
You are given: perimeter of semicircle = area of semicircle
perimeter+of+semicircle+=r%2A%28pi+%2B2%29++=+Area+of+semicircle=+%28pi%2Ar%5E2%29%2F2+
---
r%2A%28pi+%2B2%29++=+%28pi%2Ar%5E2%29%2F2+
2%2Ar%2A%28pi%2B2%29=pi%2Ar%5E2 (multiply both sides by 2)
2%2A%28pi%2B2%29=pi%2Ar (divide both sides by r)
2%2A%28pi%2B2%29%2Fpi=r (divide both sides by pi)
2%2A%28pi%2B2%29%2Fpi=2%2A%28pi%2Fpi%29%2B4%2Fpi=2%2B4%2Fpi=r

Answer by vksarvepalli(154) About Me  (Show Source):
You can put this solution on YOUR website!

The number of centimeters in the perimeter of semicircle is numerically the
same as the number of square centimeters in its area.
so pi*r = pi*r^2/2 (r is the radius of the circle)
so r=2
thus the number of centimeters in the radius of the semicircle=2