if the perimeter of a square and a circle are equal ,then what is the ratio of the side of the square and the radius of the circle
Answers
Perimeter of the square = circumference of the circle.
So, 4a = 2πr ,
where a is the length of the side of the square and r is the radius of the circle.
a = πr/2
So ,
area of the square/ area of the circle
= a²/πr²= (π².r²/⁴) πr² (using a= πr/2)
= π/4.
So the ratio of their areas= π:4
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Step-by-step explanation:
Step -1: Equate perimeter of a square and circle.
Let r be the radius of a circle
and be the side of a square.
From the given data,
Perimeter of a square = Circumference of a circle
⇒4a=2πr
⇒
r
a
=
2
π
…(1)
Step -2: Calculate the ratio of area of square and circle.
Area of circle:Area of square
⇒
Area of square
Area of circle
=
a
2
πr
2
⇒
Area of square
Area of circle
=π(
a
r
)
2
⇒
Area of square
Area of circle
=π(
π
2
)
2
(From equation (1))
⇒
Area of square
Area of circle
=π
π
2
4
⇒
Area of square
Area of circle
=
π
4
⇒
Area of square
Area of circle
=
22
4×7
(∵π=
7
22
)
⇒
Area of square
Area of circle
=
11
14
Hence, 14:11 is correct answer.
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