Question

The area of a square is 1296 cm² 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 π $=\frac{22}{7}$ ]

• A. 13 : 11
• B. 8 : 11
• C. 6 : 11
• D. 3 : 7

Answer 1

Answer:

C. 6 : 11

Solution:

Given:

Area of Square = 1296 cm²

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

Concept Used:

Area of Square = Side²

Perimeter of Square = 4 × Side

Circumference of Circle = 2πr

Calculation:

Area of Square = Side² = 1296

$Side =\sqrt{1296}=36 cm$

Now, Radius of circle $=\frac{7}{6}\times{36}=42cm$

Perimeter of Square = 4 × Side

Perimeter of Square = 4 × 36 = 144 cm

Circumference of circle = 2πr

Circumference of circle $=2\times{\frac{22}{7}}\times{42}==44\times{6}=264cm$

Ratio of Perimeter and Circumference $=\frac{144}{264}==\frac{6}{11}=6:11$

Hence, the ratio of the perimeter of square and circumference of circle is 6 : 11.