SOLUTION: A circle and a square has a same area.If c denotes circumference of circle and p denotes the perimeter of square,then (A)p>c (B)p=c (C)p<c (D)p=2c

Algebra ->  Average -> SOLUTION: A circle and a square has a same area.If c denotes circumference of circle and p denotes the perimeter of square,then (A)p>c (B)p=c (C)p<c (D)p=2c      Log On


   



Question 1076543: A circle and a square has a same area.If c denotes circumference of circle and p denotes the perimeter of square,then
(A)p>c
(B)p=c
(C)p (D)p=2c

Found 2 solutions by Alan3354, math_helper:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
For the square:
perimeter=p=4s
area = s%5E2
For the circle:
circumference = c = 2%28pi%29r
area = %28pi%29r%5E2
The areas are equal (given):
%28pi%29r%5E2+=+s%5E2
Taking sqrt of both sides:
+sqrt%28pi%29r+=+s+
Now p can be expressed in terms of r:
+p+=+4s+=+4sqrt%28pi%29r+
Since 4sqrt%28pi%29+%3E+7+ and 2%28pi%29+%3C+7+ , +highlight%28p%3Ec%29+