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The perimeter of a circle is equal to that of a square, then the ratio of their areas is

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11 : 14

10 : 11

11 : 10

14 : 11

answer is A.

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Detailed Solution

Given that, The perimeter of a circle is equal to that of a square.
Let

r

be the radius of the circle and

a

be the side of the square.
Equate the circumference of the circle with the perimeter of the square, we get

2 π r = 4 a ⇒ r = 2 a π

The area of the circle is,

A C = π r 2

And area of the square is,

A s = a 2

.
Substitute

2 a π

for

r

in the equation

A C = π r 2

and simplify the relation of the area we get,

A C = π 2 a π 2 ⇒ A C = π 4 a 2 π 2 ⇒ A C = 4 π a 2 ⇒ A C = 4 π A s

On further simplification,

A c = 4 π A S ⇒ A C A S = 4227 ⇒ A C A S = 1411

Therefore, the ratio of their areas is

14 : 11

.
Hence the correct option is 1.

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