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

Question

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

CounterSniper · Answer

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

EMPOWERgmatRichC · Answer

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.

Let's TEST Answer B: 2

IF....Radius = 2
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

IF....Radius = 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...

There's only one answer left...

Final Answer:  C

Here's proof that it's correct:

IF....Radius = 4
Circumference = 2(pi)R = 8pi
Area = (pi)R^2 = 16pi
This circumference IS half the area, so this MUST be the answer.

GMAT assassins aren't born, they're made,
Rich

KarishmaB · Answer

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

Answer (C)

Archit3110 · Answer

2 pi r= pi r^2/2

r= 4 
imo c

DisciplinedPrep · Answer

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

CareerLauncherIE · Answer

We are asked to find the radius of a circular garden if the fence around it (circumference) is  half of the area .
Let the radius of the circle be  r .
 
 The circumference of a circle = 2πr 
 The area of a circle = πr2  
The problem says:
Fence length = 1/2 × Area
So we can write:
 2πr = 1/2 × πr2
Divide both sides by π to simplify:
 2r = r2 / 2
Multiply both sides by 2 to get rid of the fraction:
 4r = r2
Rewriting:
 r2 – 4r = 0
 r(r – 4) = 0
So r = 0 (not possible) or r = 4
Hence, the radius of the garden is  4 .
 Final Answer:  (C).

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards