Question

if the perimeter of a circle is equal to that of a square then find the ratio of their area

Answer 1

perimeter of circle = perimeter of square
$2\pi \: r = 4 \times s \\ r = 4 \times s \div 2\pi \\ \frac{area \: of \: circle}{area \: of \: square} = \frac{\pi {r}^{2} }{ {s}^{2} } \\ \: \: \: \: \: \: \: \: \: \: = \ \: \pi \times \frac{4s}{2\pi} \times \frac{4s}{2\pi} \div {s}^{2} \\ = \frac{4}{\pi} = \frac{4 \times 7}{22} \\ = \frac{14}{11}$

Answer 2

Answer: Ratio would be 16:π.

Step-by-step explanation:

Since we have given that

Perimeter of the circle = perimeter of square

So, it becomes

2πr=4×s

πr=2s

r:s = 2:π

So, ratio of area of circle to area of square is given by

πr^2:s^2

π4^2:π^2

16:π

Hence, ratio would be 16:π.