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 = $\frac{22}{7}$]
Answer & explanation
Correct answer: option 3
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