The area of a square is 1296 $$cm^{2}$$ and the radius of a circle is $$\frac{7}{6}$$ of the length of a side of the square. What is the ratio of the perimeter of the square and the circumference of the circle? [Use $$\pi = \frac{22}{7}$$]

The area of a square is 1296 $$cm^{2}$$.

area of a square = $$\left(side\right)^2$$

$$1296 = \left(side\right)^2$$

length of side = 36 cm

the radius of a circle is $$\frac{7}{6}$$ of the length of a side of the square.

the radius of a circle = $$\frac{7}{6}$$ of 36 = 42 cm

Ratio of the perimeter of the square and the circumference of the circle = $$4\times side\ :\ 2\times\ \frac{22}{7}\times\ radius$$

= $$4\times36\ :\ 2\times\ \frac{22}{7}\times42$$

= $$6\ :\ 11$$