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If the circumference of a circle inscribed in a square is 25π, what is

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Bunuel
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If the circumference of a circle inscribed in a square is 25π, what is [#permalink] New post   22 Jun 2018, 01:27
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If the circumference of a circle inscribed in a square is 25π, what is the perimeter of the square?


A. 20

B. 25

C. 40

D. 50

E. 100


(PS12542)
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E
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BrentGMATPrepNow
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Re: If the circumference of a circle inscribed in a square is 25π, what is [#permalink] New post   23 Jun 2018, 09:10
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Bunuel wrote:
If the circumference of a circle inscribed in a square is 25π, what is the perimeter of the square?


A. 20

B. 25

C. 40

D. 50

E. 100


We have the following:


The perimeter of the circle = 25π

We can see that the perimeter of the square is GREATER THAN the perimeter of the circle

25π ≈ (25)(3) ≈ 75
So, the perimeter of the square is GREATER THAN 25π

Check the answer choices....only one answer choice works.

Answer: E

Cheers,
Brent
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Re: If the circumference of a circle inscribed in a square is 25π, what is [#permalink] New post   22 Jun 2018, 04:39
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Solution



Given:
    • The circumference of a circle inscribed in a square is 25π

To find:
    • The perimeter of the square

Approach and Working:
When a circle is inscribed in a square, the diameter of the circle is equal to the length of the side of the square



If r is the radius of the circle, then
    • 2πr = 25π
    Or, 2r = 25

Therefore, we can say, length of the side of the square = 25
    • Perimeter of the square = 25 * 4 = 100

Hence, the correct answer is option E.

Answer: E
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Re: If the circumference of a circle inscribed in a square is 25π, what is [#permalink] New post   22 Jun 2018, 02:13
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Answer is E.

Diameter of circle = Side of square.
Let diameter be d and side be s.
Circumference = πd = 25π
So, d = 25 = s.
Perimeter = 4s = 100

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Re: If the circumference of a circle inscribed in a square is 25π, what is [#permalink] New post   22 Jun 2018, 02:13
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πD = 25π => diameter is 25.
Therefore, side of square = 25.
Perimeter = 4*side = 100

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Re: If the circumference of a circle inscribed in a square is 25π, what is [#permalink] New post   27 Jun 2018, 18:06
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Bunuel wrote:
If the circumference of a circle inscribed in a square is 25π, what is the perimeter of the square?


A. 20

B. 25

C. 40

D. 50

E. 100


When a circle is inscribed in a square, the diameter of the circle is equal to the side of the square.

Since circumference = πd, we have:

πd = 25π

d = 25 = side of the square

Thus, the perimeter of the square is 25 x 4 = 100.

Answer: E
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Re: If the circumference of a circle inscribed in a square is 25π, what is [#permalink] New post   18 Mar 2019, 13:37
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[1] Find Diameter

Since the diameter of a circle is equal to the side of a square, finding the circle's diameter will allow us to calculate the square's perimeter.

\(Circumference = Diameter \times \pi\)

\(\frac{25\pi}{\pi} = Diameter\)

\(Diameter = 25\)

[2] Calculate Perimeter

\(Perimeter = 4 \times Side\)

\(Side \equiv Diameter\)

\(25\times 4 = 100\)

Answer E
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Re: If the circumference of a circle inscribed in a square is 25π, what is [#permalink] New post   17 Jan 2020, 21:15
The perimeter of the circle = 25π

2πr = 25π
So r= 25/2 so Diameter = 2* 25/2 = 25

So the perimeter of the square = 4a = 4* 25 = 100
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Re: If the circumference of a circle inscribed in a square is 25π, what is [#permalink] New post   02 May 2021, 22:10
Expert Reply
Bunuel wrote:
If the circumference of a circle inscribed in a square is 25π, what is the perimeter of the square?


A. 20

B. 25

C. 40

D. 50

E. 100


(PS12542)


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Answer: Option E

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Re: If the circumference of a circle inscribed in a square is 25, what is [#permalink] New post   24 Mar 2022, 08:36
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If the circumference of a circle inscribed in a square is 25, what is [#permalink] New post   15 Jun 2022, 04:58
If the circumference of a circle inscribed in a square is 25π, what is the perimeter of the square?


A. 20

B. 25

C. 40

D. 50

E. 100


Diagonal = diameter(2r) = 25, thus length of side is 25

so, perimeter is 25*4 = 100

Answer: E
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Re: If the circumference of a circle inscribed in a square is 25, what is [#permalink] New post   08 Apr 2023, 07:13
If the square is inside the circle, the perimeter of the square will be 50√2, Correct?
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Re: If the circumference of a circle inscribed in a square is 25, what is [#permalink] New post   03 Jun 2023, 05:58
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius of the circle.

In this case, we are given that the circumference of the circle inscribed in a square is 25π. Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square.

Let's denote the side length of the square as s. Therefore, the diameter of the circle is also s, and the radius of the circle is s/2.

We can set up the equation for the circumference of the circle:

C = 2πr
25π = 2π(s/2)
25 = s

Therefore, the side length of the square is 25.

To find the perimeter of the square, we can multiply the side length by 4:

Perimeter = 4s = 4 * 25 = 100

Therefore, the perimeter of the square is 100, which corresponds to option (E).
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Re: If the circumference of a circle inscribed in a square is 25, what is [#permalink]
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