Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Jun 1006:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..- Jun 10
10:00 AM PDT
-11:00 AM PDT
Scoring 715 on the GMAT Focus Edition requires more than just learning formulas, memorizing concepts, or solving hundreds of questions. In this episode, Nishant shares how he improved his GMAT preparation by focusing on application of concepts, and more. 
Jun 1111:00 AM EDT
-01:00 PM EDT
TTP GMAT OnDemand gives serious students 400+ hours of expert video instruction, the full TTP course, AI support, weekly office hours, and a 715+ score guarantee—all built for elite GMAT score improvement.
Jun 2207:30 PM EDT
-09:30 PM EDT
Master the GMAT with expert live instruction, a personalized study plan, and real-time support. Includes 40 hours of online classes plus 6 months of access to the TTP GMAT OnDemand video course. Class date: Mon/Wed June 22, 2026 →August 26, 2026
19 Dec 2010, 07:29
Kudos
Bookmarks
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
71% (00:41) correct
29%
(00:49)
wrong
based on 22
sessions
History
Date
Time
Result
Not Attempted Yet
The area of a rectangle inscribed in a circle is 12. Area of the circle is 25/4 pi. What is the perimeter of the rectangle?
19 Dec 2010, 08:00
Kudos
Bookmarks
smitakokne
As explained by Karishma below it should be: \(area_{rectangle}=ab=12\) instead of 24.
Given: \(area_{circle}=\pi{r^2}=\frac{25}{4}*\pi\) --> \(r=2.5\) and \(area_{rectangle}=ab=12\), where \(a\) and \(b\) are the lengths of the sides of the rectangle.
Question: \(perimeter_{rectangle}=2(a+b)=?\)
Now, a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.
A diagonal of a rectangle is the hypotenuse for its sides, so as rectangle is inscribed in a circle then its diagonal is the diameter of the circle. Which means that \(diagonal=diameter=2*radius=5\). Also \(d^2=25=a^2+b^2\).
Now, square \(perimeter_{rectangle}=2(a+b)\) --> \(P^2=4(a^2+2ab+b^2)\), as given that \(ab=12\) and \(25=a^2+b^2\) then \(P^2=4(a^2+2ab+b^2)=4(25+24)=4*49\) --> \(P=\sqrt{4*49}=2*7=14\).
Answer: \(14\).
Hope its clear.
smitakokne
25/4 pi is around 20. The area of inscribed rectangle cannot be more than this so it cannot be 24. From the way this question is formed, I would expect the area of the rectangle to be 12. (I will explain this later). I will solve the question assuming this value of area.
Area of circle = 25/4 pi = pi*r^2
Radius of circle = 5/2 and diameter is 5.
The rectangle inscribed in the circle will have its center at the center of the circle since its opposite sides are equal and parallel. The diagram below will show you why it should be so.
Attachment:
Ques1.jpg [ 7.04 KiB | Viewed 6853 times ]
So diameter of the circle should be the diagonal of the rectangle i.e. 5.
So area of rectangle = ab = 12
and \(a^2 + b^2 = 5^2\) (pythagorean theorem)
The most common pythagorean triplet is 3,4,5 and since the diagonal was 5, I was looking for the sides to be 3 and 4 possibly giving the area as 12. In GMAT, numbers fall in place very well)
Sides must be 3 and 4 giving the perimeter as 2(3+4) = 14
