BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Rectangular garden Alpha and circular pond Beta have equal

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2276
Joined: Sat Oct 14, 2017 6:10 am
Followed by:3 members

Rectangular garden Alpha and circular pond Beta have equal

by VJesus12 » Thu May 03, 2018 10:46 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Rectangular garden Alpha and circular pond Beta have equal area. If garden Alpha is 9 meter by 6 meters, what is the radius of pond Beta?

A) 54Ï€
B) 54/Ï€
C) √(54/π)
D) √(27/π)
E) 27Ï€

The OA is the option C.

What is the formula that helps me here? Can anyone remind it to me? Please.
Top
Source: — Problem Solving |
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

by Vincen » Thu May 03, 2018 12:08 pm
Hello vjesus12.

Here, you just have to use the area of a rectangular region and a circular region, that is to say: $$A_R=w\cdot l\ \ \ \ \ \ \ and\ \ \ \ \ \ \ \ A_C=\pi\ r^2\ .$$ We know that the dimensions of the rectangular region are 9 and 6. Then $$A_R=9\cdot6\ \ \ \ \ \ \ and\ \ \ \ \ \ \ \ A_C=\pi\ r^2 $$ $$A_R=54\ \ \ \ \ and\ \ \ \ \ \ \ \ A_C=\pi\ r^2\ .$$ In addition, we know that both regions have the same area, then $$A_R=54\ =\pi\ r^2\ =\ A_C$$ $$\Rightarrow\ \ \ \ r^2=\frac{54}{\pi}$$ $$\Rightarrow\ \ \ \ r=\sqrt{\frac{54}{\pi}}.$$ It implies that the correct asnwer is the option C .

I hope this explanation may help you.
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Mon May 07, 2018 10:23 am
VJesus12 wrote:Rectangular garden Alpha and circular pond Beta have equal area. If garden Alpha is 9 meter by 6 meters, what is the radius of pond Beta?

A) 54Ï€
B) 54/Ï€
C) √(54/π)
D) √(27/π)
E) 27Ï€
The area of Alpha is 9 x 6 = 54. So we use the equation for the area of a circle to determine the radius, r, of Beta:

54 = πr^2

54/Ï€ = r^2

√(54/π) = r

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Legendary Member
Posts: 2499
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members

by swerve » Tue May 08, 2018 8:16 am
Area of rectangular garden A is L * W = 54

Area of circular pond B = π*r^2

Areas are equal

54 = π*r^2

54/Ï€ = r^2

√(54/π) = r

Option C.
Top
Post new topic Post Reply
• Page 1 of 1