Question

if the perimeter of a circle is equal to that of a square then the ratio of their areas is​

Answer 1

Answer:

Given Perimeter of circle is equal to perimeter of square

i.e

2πr = 4a

=> a = (2πr)/4

=> a = πr/2

Area of circle ,a1 = π$r^{2}$

Area of square, a2 = $a^{2}$

then , their ratio:

a1/a2 = π$r^{2}$/ $a^{2}$

=>  π$r^{2}$ /  (π$r/2)^{2}$

=>  4π$r^{2}$/ π^2 $r^{2}$

=> 4/ π

Therefore the ratio of a1/a2 = 4/π

or a1:a2 = 4:π

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Step-by-step explanation: