Question

if the area of the square is same as the area of the circle find the ratio of the perimeter of the square and that of circle??​

Answer 1

let the side of the square be 'a'

area=

${a}^{2}$

let the radius of circle be 'r'

area=

$\pi {r}^{2}$

given that:-

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

perimeter of square=4a

perimeter of circle=

$2\pi \:r$

ratio of the perimeter of the square and that of circle is:-

$\frac{4a}{2\pi \: r} \\ \frac{2a}{\pi \: r} \\ we \: know \: by \: our \: previous \: derivation \: that \\ \frac{a}{r} = \sqrt{\pi} \\ using \: this \: in \: the \: ratio \\ \frac{2 \sqrt{\pi} }{\pi} \\ ratio = 2 : \sqrt{\pi}$

Answer 2

Answer:Let the radius of the circle be r and the side of the square be a.

Then according to the question, πr2=a2=>a=rπ−−√

(i) Now , Ratio of their perimeters =2πr4a

Ratio of their perimeters =πr2a

=πr2rπ−−√

=π−−√2

Ratio of their perimeters =π−−√:2

Step-by-step explanation:ask me if you don't understand...