Question

20. If the perimeter of a circle is equal to that of a square, then the ratio of their
areas is​

Answer 1

Answer:

Hence the ratio of Area of a circle to that of a square is π4.

Answer 2

GIVEN:-

• Perimeter of the circle is equal to that of a square

TO FIND:-

• The ratio of their area

SOLUTION:-

Given that Perimeter of circle is equal to perimeter of square

2πr = 4a

$\frac{r}{a} = \frac{4}{2\pi} = \frac{2}{\pi} \\ \\ \frac{area \: of \: circle}{area \: of \: square} = \frac{\pi {r}^{2} }{ {a}^{2} } = \pi( { \frac{r}{a} })^{2} \\ \\ using \: \: \frac{r}{a} = \frac{2}{\pi} \\ \\ we \: get \\ \frac{area \: of \: circle}{area \: of \: square} = \pi( { \frac{2}{\pi} })^{2} \\ = \frac{4}{ {\pi}^{2} } \times \pi = \frac{4}{\pi}$

Hence the ratio of area of a circle to that of the square is 4/π

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