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Math Expert V
Joined: 02 Sep 2009
Posts: 59587
If the circumference of a circle inscribed in a square is 25π, what is  [#permalink]

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13 00:00

Difficulty:   5% (low)

Question Stats: 79% (00:56) correct 21% (00:56) wrong based on 935 sessions

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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

NEW question from GMAT® Official Guide 2019

(PS12542)

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Intern  B
Joined: 21 May 2017
Posts: 42
Re: If the circumference of a circle inscribed in a square is 25π, what is  [#permalink]

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2

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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Intern  B
Joined: 03 Aug 2014
Posts: 19
Schools: Kellogg '21 (A)
Re: If the circumference of a circle inscribed in a square is 25π, what is  [#permalink]

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1
πD = 25π => diameter is 25.
Therefore, side of square = 25.
Perimeter = 4*side = 100

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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Re: If the circumference of a circle inscribed in a square is 25π, what is  [#permalink]

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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.

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GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4125
Re: If the circumference of a circle inscribed in a square is 25π, what is  [#permalink]

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Top Contributor
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

Cheers,
Brent
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Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: If the circumference of a circle inscribed in a square is 25π, what is  [#permalink]

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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.

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Intern  B
Joined: 01 Mar 2019
Posts: 19
Location: United States
If the circumference of a circle inscribed in a square is 25π, what is  [#permalink]

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 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.

$$Circumference = Diameter \times \pi$$

$$\frac{25\pi}{\pi} = Diameter$$

$$Diameter = 25$$

 Calculate Perimeter

$$Perimeter = 4 \times Side$$

$$Side \equiv Diameter$$

$$25\times 4 = 100$$ If the circumference of a circle inscribed in a square is 25π, what is   [#permalink] 18 Mar 2019, 13:37
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