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The perimeter of a square is P cm and the area of the circle which is
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02 May 2023, 07:21
02 May 2023, 07:21
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The perimeter of a square is P cm and the area of the circle which is inscribed in it, is A cm2. If P = 4A, then what is the length of the side of the square?
\(\frac{4}{\pi}\)
\(\frac{12}{\pi}\)
\(\frac{14}{\pi}\)
\(\frac{16}{\pi}\)
\(2 \pi\)
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE GEOMETRY
\(\frac{4}{\pi}\)
\(\frac{12}{\pi}\)
\(\frac{14}{\pi}\)
\(\frac{16}{\pi}\)
\(2 \pi\)
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE GEOMETRY
The perimeter of a square is P cm and the area of the circle which is
[#permalink]
28 May 2023, 00:33
28 May 2023, 00:33
Expert Reply
OE
GRE square (2).jpg [ 13.11 KiB | Viewed 1068 times ]
Let the length of the square = x cm
Let the radius of the circle = r cm
The circle is inscribed in the square, so side of the square = Diameter of the circle
Diameter of circle = 2r
So, x = 2r
r = 𝑥/2…………………………………………………………. (1)
The perimeter of square = P cm = 4x
Area of the circle = A cm^2 = πr^2
As, P = 4A4x = 4(πr^2)
x = πr^2
Putting the value of r from equation (1),
x = π(𝑥^2/4)
πx^2 = 4x
πx^2 – 4x = 0
x (π x – 4) = 0
So, either x = 0 OR x = 4/𝜋
But x cannot be 0
So, x = 4/𝜋
Ans. (A)
Attachment:
GRE square (2).jpg [ 13.11 KiB | Viewed 1068 times ]
Let the length of the square = x cm
Let the radius of the circle = r cm
The circle is inscribed in the square, so side of the square = Diameter of the circle
Diameter of circle = 2r
So, x = 2r
r = 𝑥/2…………………………………………………………. (1)
The perimeter of square = P cm = 4x
Area of the circle = A cm^2 = πr^2
As, P = 4A4x = 4(πr^2)
x = πr^2
Putting the value of r from equation (1),
x = π(𝑥^2/4)
πx^2 = 4x
πx^2 – 4x = 0
x (π x – 4) = 0
So, either x = 0 OR x = 4/𝜋
But x cannot be 0
So, x = 4/𝜋
Ans. (A)
gmatclubot
The perimeter of a square is P cm and the area of the circle which is [#permalink]
28 May 2023, 00:33
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