Question

if perimeter of a square is 2x , and area of this square is equal to area of circle , find perimeter of the circle. Pls answer with correct explanation. ​

Answer 1

Answer:

2x

Step-by-step explanation:

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Answer 2

Answer:

perimeter of the circle is $x\sqrt{\pi}$

Step-by-step explanation:

Given,

         Perimeter of a square is $2x.$

Let us consider the side of the square be $a$

We know that,

Perimeter of the square =$4a$

So,

       $4a=2x\\ \\ a=\frac{2x}{4}=\frac{x}{2}$

Area of the square is given by

      Area of the square =$a^2$

                                       =$(\frac{x}{2})^2 =\frac{x^2}{4}$

Let the radius of the circle be R.

so area of the circle =$\pi R^2$

Area of this square is equal to area of circle.

$\pi R^2=a^2\\ \\ R^2=\frac{a^2}{\pi} \\ \\ R=\frac{a}{\sqrt{\pi} }$

perimeter of the circle=$2 \pi R$

                                      =$2 \pi \frac{a}{\sqrt{\pi} } \\ \\ =2a\sqrt{\pi}\\ \\ =2 \cdot \frac{x}{2}\cdot \sqrt{\pi} \\ \\ =\sqrt{\pi}x$