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# help

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If a square and a regular hexagon have equal areas, then find the ratio of their perimeters.

Dec 9, 2019

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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   Dec 9, 2019