The area of a square is 1296 cm² and the radius of a circle is $\frac{6}{7}$ 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 π = $\frac{22}{7}$]

6 : 11

The area of a square =1296 cm²

The radius of a circle = $\frac{6}{7}$ of the length of a side of the square

We know that,

Area of Square = Side²

Perimeter of Square = 4 × Side

Circumference of Circle = 2πr

So,

Area of Square = Side² = 1296

Side = 32

Perimeter of Square = 4 × Side

Perimeter of Square = 4 × 36 = 144 cm

The radius of a circle = $\frac{7}{6}$ × 36 = 42

Circumference of Circle = 2 × \(\frac{22}{7}\) × 42 = 264 cm

Ratio of Perimeter and Circumference = 144 : 264 = 6 : 11