Rectangular garden Alpha and circular pond Beta have equal

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

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

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) âˆš(54/Ï€)
D) âˆš(27/Ï€)
E) 27Ï€

The OA is the option C.

What is the formula that helps me here? Can anyone remind it to me? Please.

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Source: Beat The GMAT — Problem Solving | Thu May 03, 2018 10:46 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

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.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

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) âˆš(54/Ï€)
D) âˆš(27/Ï€)
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 = Ï€r^2

54/Ï€ = r^2

âˆš(54/Ï€) = r

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed 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 = Ï€*r^2

Areas are equal

54 = Ï€*r^2

54/Ï€ = r^2

âˆš(54/Ï€) = r

Option C.

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