Question

If a square and a circle have the same perimeter then

• A. the area of the circle is greater than that of square
• B. the area of the square is greater than that of circle
• C. the area of the square is $1/\pi$ times that of the circle.
• D. their areas are equal

Answer 1

The correct option is A the area of the circle is greater than that of square

Let the perimeter of circle and square is 1

Then perimeter of circle =$2\pi r=1$( where r is redius of circle)

$\Rightarrow r=\frac{1}{2\pi }$

Then area of circle =$\pi r^2=\pi (\frac{1}{2\pi }{)}^2=\frac{1}{4\pi }=0.0795$

perimeter of square =4l=1 then l=$\frac{1}{4}$ (where l id the side of square)

Then area of square=$\frac{1}{4}\times \frac{1}{4}=\frac{1}{16}=0.0625$

Then area of circle is greater then that of squre