SOLUTION: Express the length of the perimeter of a circle in terms of the area of the circle. Use A for the area in your answer. Perimeter = ? Thanks so much for the help!

Algebra ->  Circles -> SOLUTION: Express the length of the perimeter of a circle in terms of the area of the circle. Use A for the area in your answer. Perimeter = ? Thanks so much for the help!      Log On


   

Question 255740: Express the length of the perimeter of a circle in terms of the area of the circle. Use A for the area in your answer. Perimeter = ?
Thanks so much for the help!
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter of a circle, also circumference is
(i) C+=+2%2Api%2Ar
The area of a circle is
(ii) A+=+pi%2Ar%5E2
solve the area formula for r and we get
(iii) a%2Fpi+=+r%5E2
(iv) sqrt%28A%2Fpi%29+=+r
substitute (iv) into (i) to get
C+=+2%2Api%2Asqrt%28A%2Fpi%29
which is simplified to
C+=+2sqrt%28A%2A%28pi%29%29