Question

What is the perimeter of a square whose area is equal to that of a circle with perimeter $2\pi x$?

• A. $2\pi x$
• B. $\sqrt{\pi }x$
• C. $4\sqrt{\pi x}$
• D. $4x\sqrt{\pi }$

Answer 1

The correct option is D $4x\sqrt{\pi }$

Radius of the circle with perimeter $2\pi x$$=\frac{2\pi x}{2\pi }=x$

$\therefore$ It's area $=\pi x^2$

Area of square with side $a=a^2=\pi x^2\Rightarrow a=x\sqrt{\pi }$

$\therefore$ Perimeter of square $=4a=4x\sqrt{\pi }$