SOLUTION: Three shapes- a circle, a rectangle, and a square- have the same area. Which shape has the smallest perimeter?

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Question 556429: Three shapes- a circle, a rectangle, and a square- have the same area. Which shape has the smallest perimeter?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Circle -- a bit tricky to prove using elementary geometry techniques, but we can definitely find an example. For example, suppose that the area of each shape is 1. It can easily be shown that the rectangle with fixed area and the minimal perimeter is a square. The perimeter of the square is 4, and now you can just find the radius of the circle with area 1, then find the circumference.