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# A circular garden is surrounded by a fence of negligible width along

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Math Expert
Joined: 02 Sep 2009
Posts: 56260
A circular garden is surrounded by a fence of negligible width along  [#permalink]

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08 Dec 2015, 02:57
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:03) correct 23% (01:29) wrong based on 86 sessions

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A circular garden is surrounded by a fence of negligible width along the boundary. If the length of the fence is 1/2 of th area of the garden. What is the radius of the circular garden?

A. 1
B. 2
C. 4
D. 8
E. 16

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Re: A circular garden is surrounded by a fence of negligible width along  [#permalink]

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08 Dec 2015, 03:07
as per the question-- width is negligible

now,
let L be the length of the fence =2pir
L=1/2(pir^2)
pir^2=4pir
r=4
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Re: A circular garden is surrounded by a fence of negligible width along  [#permalink]

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08 Dec 2015, 18:06
Hi All,

This question can be solved algebraically or by TESTing THE ANSWERS.

We're told that the circumference of a circular garden = 1/2 the area of the garden. We're asked for the RADIUS of the garden.

Circumference = 2(pi)R = 4pi
Area = (pi)R^2 = 4pi
This circumference is NOT half the area.
Eliminate Answer B. We need the area to be BIGGER...

Next, Let's TEST Answer D: 8

Circumference = 2(pi)R = 16pi
Area = (pi)R^2 = 64pi
This circumference is NOT half the area (it's 1/4 of the area).
Eliminate Answer D. We need the area to be SMALLER...

Here's proof that it's correct:

Circumference = 2(pi)R = 8pi
Area = (pi)R^2 = 16pi
This circumference IS half the area, so this MUST be the answer.

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Re: A circular garden is surrounded by a fence of negligible width along  [#permalink]

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21 Dec 2018, 22:15
1
Bunuel wrote:
A circular garden is surrounded by a fence of negligible width along the boundary. If the length of the fence is 1/2 of th area of the garden. What is the radius of the circular garden?

A. 1
B. 2
C. 4
D. 8
E. 16

Fence of negligible width surrounding the garden will have the same length as the circumference of the circular garden.
$$Length = 2*\pi*r$$

This is half of the area of the garden which is $$\pi*r^2$$

Hence,
$$2*\pi*r = \frac{1}{2}*\pi*r^2$$
$$r = 4$$

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Re: A circular garden is surrounded by a fence of negligible width along  [#permalink]

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22 Dec 2018, 09:24
Bunuel wrote:
A circular garden is surrounded by a fence of negligible width along the boundary. If the length of the fence is 1/2 of th area of the garden. What is the radius of the circular garden?

A. 1
B. 2
C. 4
D. 8
E. 16

2 pi r= pi r^2/2

r= 4
imo c
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Re: A circular garden is surrounded by a fence of negligible width along  [#permalink]

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22 Dec 2018, 09:53
Bunuel wrote:
A circular garden is surrounded by a fence of negligible width along the boundary. If the length of the fence is 1/2 of th area of the garden. What is the radius of the circular garden?

A. 1
B. 2
C. 4
D. 8
E. 16

Formula based question and test takers should be able to complete such questions in less than 60 sec.
Length of the fence = length of the circular garden = circumference of the circular region = 2πr
According to the condition, length of the fence is 1/2 of the area of the garden (πr^2)
Therefore, 2πr = 1/2 x (πr^2)
Solving the above equation, r = 4

Hence, the answer is option C. 4

Tip: Always write what you're solving for. Sometimes questions ask you to find diameter, or some other value. Do no blindly solve such each questions because there're some deadly traps
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Re: A circular garden is surrounded by a fence of negligible width along   [#permalink] 22 Dec 2018, 09:53
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