NEW HERE? LEARN MORE
closeclose
Last visit was: 04 May 2024, 23:13 It is currently 04 May 2024, 23:13
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A 3 by 4 rectangle is inscribed in a circle. What is the area of the

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93029
Own Kudos [?]: 621252 [0]
Given Kudos: 81745
Send PM
CAT Tests Forum Quiz Mode
A 3 by 4 rectangle is inscribed in a circle. What is the area of the [#permalink] New post   20 Nov 2017, 23:20
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

87% (00:45) correct 13% (01:01) wrong based on 45 sessions
Hide Show timer Statistics
A 3 by 4 rectangle is inscribed in a circle. What is the area of the circle?

(A) 6.25π
(B) 9π
(C) 12.25π
(D) 16π
(E) 25π
ShowHide Answer
Official Answer
A
User avatar
P
rahul16singh28
Senior Manager
Senior Manager
Joined: 31 Jul 2017
Posts: 435
Own Kudos [?]: 443 [0]
Given Kudos: 752
Location: Malaysia
Schools: INSEAD Jan '19
GPA: 3.95
WE:Consulting (Energy and Utilities)
Send PM
Re: A 3 by 4 rectangle is inscribed in a circle. What is the area of the [#permalink] New post   20 Nov 2017, 23:26
\sqrt{}
Bunuel wrote:
A 3 by 4 rectangle is inscribed in a circle. What is the area of the circle?

(A) 6.25π
(B) 9π
(C) 12.25π
(D) 16π
(E) 25π


l = 3, b = 5
2r = 5... A= 6.25pi
User avatar
L
Skywalker18
Verbal Forum Moderator
Joined: 08 Dec 2013
Status:Greatness begins beyond your comfort zone
Posts: 2100
Own Kudos [?]: 8821 [0]
Given Kudos: 171
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
Send PM
GMAT ToolKit User Reviews Badge
Re: A 3 by 4 rectangle is inscribed in a circle. What is the area of the [#permalink] New post   21 Nov 2017, 01:06
Bunuel wrote:
A 3 by 4 rectangle is inscribed in a circle. What is the area of the circle?

(A) 6.25π
(B) 9π
(C) 12.25π
(D) 16π
(E) 25π


The diagonal of the rectangle is 5 since we have pythagoras right triangle 3-4-5 .
This diagonal is the diameter of the circle .
Area = pi* (5/2)^2 = 6.25 pi

Answer A
avatar
B
pulkitarya
Intern
Intern
Joined: 16 Aug 2016
Posts: 13
Own Kudos [?]: 10 [0]
Given Kudos: 40
Location: India
Schools: IIMA IIMA PGPX'22 ISB'22 HEC ESSEC GMBA '22
GMAT 1: 530 Q39 V25
GPA: 3.6
WE:Sales (Retail)
Send PM
GMAT ToolKit User
Re: A 3 by 4 rectangle is inscribed in a circle. What is the area of the [#permalink] New post   21 Nov 2017, 01:15
A rectangle being inscribed in a circle means that the diagonal of the rectangle will become the diameter of the circle.

Diagonal of a rectangle = \(\sqrt{L^2 + B^2}\) => \(\sqrt{4^2 + 3^2}\) => \(\sqrt{16+9}\) => \(\sqrt{25}\) = 5
As in this case, diagonal = diameter, hence, radius of the circle becomes 2.5

Area of a circle = \(\pi\)\(r^2\) => \(\pi\)*\(2.5^2\) => 6.25\(\pi\)
Option A
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6070
Own Kudos [?]: 4696 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Re: A 3 by 4 rectangle is inscribed in a circle. What is the area of the [#permalink] New post   21 Nov 2017, 08:31
Bunuel wrote:
A 3 by 4 rectangle is inscribed in a circle. What is the area of the circle?

(A) 6.25π
(B) 9π
(C) 12.25π
(D) 16π
(E) 25π

Diagonal of the rectangle = Diameter of the Circle.

Diameter of the rectangle is 5 ( As Its a right angled triangle with sides 3,4,5)

So, Radius is \(2.5\)

Thus, area will be \(2.5^2π\) = \(6.25π\) , answer will be (A)
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6310 [0]
Given Kudos: 1646
Send PM
Forum Quiz Mode
Re: A 3 by 4 rectangle is inscribed in a circle. What is the area of the [#permalink] New post   27 Nov 2017, 11:50
Expert Reply
Bunuel wrote:
A 3 by 4 rectangle is inscribed in a circle. What is the area of the circle?

(A) 6.25π
(B) 9π
(C) 12.25π
(D) 16π
(E) 25π


When a rectangle is inscribed in a circle, its diagonal is equal to the diameter of the circle. Furthermore, the diagonal of the rectangle divides the rectangle into two congruent right triangles with the diagonal being the hypotenuse. Since the two legs of the right triangle are 3 and 4,respectively, the hypotenuse must be 5, and thus, the diameter of the circle is 5, and the radius is 2.5. Therefore, the area of the circle is:

(2.5)^2 x π = 6.25π

Answer: A
GMAT Club Bot
gmatclubot
Re: A 3 by 4 rectangle is inscribed in a circle. What is the area of the [#permalink]
27 Nov 2017, 11:50
Moderators:
Bunuel
Math Expert
93029 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions