SOLUTION: A square and a circle have equal areas. Which shape has shorter perimeter?

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Question 180623: A square and a circle have equal areas. Which shape has shorter perimeter?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The square has an area of A%5Bs%5D=s%5E2 and a perimeter of P%5Bs%5D=4s.
The circle has an area of A%5Bc%5D=pi%2Ar%5E2 and a perimeter of P%5Bc%5D=2%2Api%2Ar.
If the areas are equal then,
A%5Bs%5D=A%5Bc%5D
s%5E2=pi%2Ar%5E2
s=sqrt%28pi%29%2Ar
The perimeter of the square would then be
P%5Bs%5D=4s=4%2Asqrt%28pi%29%2Ar while the perimeter of the circle is
P%5Bc%5D=2%2Api%2Ar
.
.
.
4%2Asqrt%28pi%29=7.09
2%2Api=6.28
.
.
.
The circle has the shorter perimeter.