Question

The perimeter of a circular plot is equal to that of a square plot What is the ratio of their respective areas

• A. $14:11$
• B. $11:14$
• C. $7:11$
• D. None of these

Answer 1

Answer: (A)

$14:11$

Let 4x be the perimeter of the square so that its area is $x^2$
circumfrence =$2\pi r=4x$
$\therefore r=\frac{2x}{\pi }$
$\therefore$ Area=$\pi r^2=\pi {\left(\frac{2x}{\pi }\right)}^2$
$=\pi \frac{4}{{\pi }^2}{x}^2$
$\therefore$ Ratio of the circle and the square
$=\frac{4}{\pi }{x}^2:x^2$
$=4:\pi or4:\frac{22}{7}$
$=28:22or14:11$