GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
The perimeter of a square is P cm and the area of the circle which is
[#permalink]
02 May 2023, 07:21
02 May 2023, 07:21
Expert Reply
00:00
Question Stats:
100% (02:15) correct
0% (00:00) wrong based on 8 sessions
Hide Show timer Statistics
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 1533 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 1533 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
Moderators:
