Question

If the perimeter of square is equal to the circumference of cicrle . Find the ratio of their areas

Answer 1

I hope it helps you.......

Answer 2

Let side of square is s,
and radius of the circle is r. Then,
perimeter of the square is = 4s
circumference of the circle is = 2πr
given,
perimeter of square = circumference of circle
$= > 4s \: = \: 2 \: \pi \: r \\ = > s = \frac{\pi \: r}{2}$
By the condition,
ratio of area of square and circumference =
$\frac{area \: of \: square}{area \: of \: circle} = \frac{ {s}^{2} }{\pi \: {r}^{2} } \\ = \frac{ { (\frac{\pi \: r}{2} )}^{2} }{\pi \: {r}^{2} } = \frac{ {\pi}^{2} \: {r}^{2} }{4 \: \pi \: {r}^{2} } \: = \frac{\pi}{4}$
= π : 4
Therefore, ratio of there areas is π : 4.