Here Is An Alternate Version Of The Question's Answer -

Let 'a' Be The Length Of Side Of The Square.

Now,

Since 36π - 18 Is The Area Of the Circle - Area Of the Square Present. This Can Be Represented As -

36π - 18 = πr^2 - a^2

So, πr^2 = 36π - 18 + a^2

Now, The Diagonal Of The Square From The Centre Can Be Considered As The Radius Of The Circle. Also WE Know The Angles Of A Square Measure 90. Therefore By Pythagoras Theorem -

a^2 + b^2 = c^2

a = side of square, b = side of square, c = radius. In a Square Sides Are Equal So a=b.

therefore, r^2 = 2a^2

Putting This In our Equation

2πa^2 = 36π - 18 + a^2

2πa^2 - a^2 = 36π - 18

Putting Pi As 22/7 -

44/7*a^2 - a^2 = 36*22/7 - 18

44a^2 - 7a^2 / 7 = 792 - 126 / 7 (Taking LCM = 7)

So, 7 Gets Cancelled Therefore, 37a^2 = 666

Now a^2 = 666/37 = 18

so a = root 18 = 3√ 2

Therefore One Side Of The Square = 3√ 2

So the Perimeter = 4a^2 = 4 * 3 * √ 2 = 12√ 2

Hope You Find The Answer Useful.

Cheers.