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# The figure shown represents a piece of land that is in the

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Manager
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The figure shown represents a piece of land that is in the [#permalink]  02 Sep 2007, 18:52
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Question Stats:

76% (01:45) correct 24% (00:29) wrong based on 176 sessions
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fence.gif [ 2.44 KiB | Viewed 6620 times ]
The figure shown represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?

(A) 278
(B) 341
(C) 357
(D) 400
(E) 441
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Jul 2013, 07:15, edited 2 times in total.
Edited the question and moved to PS forum.
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r = 100
Length of arc = 2(pi)(100)/4 = 50pi = ~150

Fencing needed = ~350. Ans C
Director
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The Central Angle of the Circle is 90.
The length of the Arc = (90/360) * Circumference of the Circle
= 2* pi * 100 / 4 = 2 * pi * 25 = 50 * 3.14 = 157

Perimeter of the Arc = 100 + 100 + 157 = 357
Senior Manager
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Just C, from 2PR=circumference and multiplied by 1/4 + 200

Ans: C
Manager
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Re: GMATPrep Question -- Land enclosed by fence? [#permalink]  04 Sep 2007, 22:11
Length = [(2.pi.r)/4+2r] = r(pi+4)/2=r(3.14+4)/2=r x 3.57
When r is 100, length will be 357

Regards.

humtum0 wrote:
The figure represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence , which of the following is the closest to the length , in feet, of the fence?

A. 278
B. 341
C. 357
D. 400
E. 441

OA ----> C

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Re: GMATPrep Question -- Land enclosed by fence? [#permalink]  06 Sep 2007, 20:14
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humtum0 wrote:
The figure represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence , which of the following is the closest to the length , in feet, of the fence?

A. 278
B. 341
C. 357
D. 400
E. 441

OA ----> C

Wish I got this on my gmatprep. If u know the rules of circles and what not, this is a gimme problem.

Essentially the question is asking us for the perimeter of the quarter circle.

P= Side1+side2+arc length of the 1/4 circle. radius is 100ft so the diameter is 200ft.

Circum=200pi.

to find the arc length take the degrees of the center of the circle given here as 90degrees and divide it by the total degrees of the circle. So 90/360=1/4.

1/4*200pi=50pi

P=100+100+50pi ---> 200+50pi. U must know that pi is rougly 3.14 or even just 3. so 200+150=350. Closest answer to this is C.
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Re: The figure represents a piece of land that is in the shape [#permalink]  24 Jul 2013, 05:55
The way I did this one was the maximum value if we draw a square would be 400

and if we use Pythagorean theorem we get 100 + 100 + 100 $$\sqrt{2}$$

The value will be greater than this and less than 400 so answer is 357

any other alternative methods to solve this question?
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Re: The figure shown represents a piece of land that is in the [#permalink]  11 Sep 2014, 11:41
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Re: The figure shown represents a piece of land that is in the   [#permalink] 11 Sep 2014, 11:41
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