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If the circumference of a circle and the perimeter of a square are equal, then,

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Area of the circle

=

Area of the square

Area of the circle

>

Area of the square

Area of the circle

<

Area of the square

Nothing definite can be said about the relation between the areas of the circle and square.

answer is B.

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Detailed Solution

Given that, the circumference of a circle and the perimeter of a square are equal.
Let

r

be the radius of the circle and

a

be the side of the square.

C i r c u m f e r e n c e of the circle = Perimeter of the square

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.

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

The value of

4 π

is more than

1

, so the area of the circle is more than the area of the square.
Hence option 2) is correct.

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