If a square and a regular hexagon have equal areas, then find the ratio of their perimeters.
+128406 Area of square = [Side of Square ] ^2
Area of hexagon = [Side of Hexagon]^2 * 3√3 / 2
So
[ Side of Square] ^2 = [ Side of Hexagon] ^2 (3/2)√3
[ Side of Square ]^2
___________________ = (3/2)√3 = (1.5)√3 take both roots
[ Side of Hexagon] ^2
Side of Square
______________ = √[ 1.5√3 ]
Side of Hexagon
So......the Side of the square = √[1.5√3 ] * Side of the Hexagon
So......the perimeter of the Square = 4√[ 1.5√3] * Side of Hexagon
Let the Side of the Hexagon = A
So.....
The perimeter of the Square = 4√[ 1.5√3] * A
And the perimeter of the Hexagon = 6A
So
Perimeter of Square 4*√[ 1.5√3] * A 2 √[ 1.5√3]
_________________ = _____________ = __________
Perimeter of Hexagon 6A 3
