A square and a circle, both have the same perimeter. Which has the largest area?

Answer 1

let one side of the square be s and let the radius of the circle be r:

the perimeter of the square = the perimeter of the circle

4s = 2πr, so s = (πr/2)

area of square = s² = (πr/2)² = (π/2)²r² = 2.47r² < area of circle = πr² = 3.14r²