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.
Nov 1912:30 PM EST
-01:30 PM EST
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more
Nov 2007:30 AM PST
-08:30 AM PST
Learn what truly sets the UC Riverside MBA apart and how it helps in your professional growth
Nov 2001:30 PM EST
-02:30 PM IST
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2407:00 PM PST
-08:00 PM PST
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
16 Sep 2014, 01:17
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
60% (02:12) correct
40%
(02:45)
wrong
based on 178
sessions
History
Date
Time
Result
Not Attempted Yet
Is the area of a rectangle inscribed in a circle with a radius of 5 centimeters greater than 48 square centimeters?
(1) The ratio of the lengths of the rectangle's sides is 3:4..
(2) The difference between the lengths of the rectangle's two adjacent sides is less than 3 centimeters.
(1) The ratio of the lengths of the rectangle's sides is 3:4..
(2) The difference between the lengths of the rectangle's two adjacent sides is less than 3 centimeters.
16 Sep 2014, 01:17
Kudos
Bookmarks
Official Solution:
Is the area of a rectangle inscribed in a circle with a radius of 5 centimeters greater than 48 square centimeters?
Refer to the diagram below:
A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. Since a rectangle comprises two right triangles, a rectangle inscribed in a circle must have its diagonal as the diameter of the circle.
Given: \(radius=5\), hence \(diameter=diagonal=10\).
Question: \(area=ab=?\) (where \(a\) and \(b\) are the sides of the rectangle).
(1) The ratio of the lengths of the rectangle's sides is 3:4.
Given that \(\frac{a}{b}=\frac{3x}{4x}\), for some positive multiplier \(x\). Therefore, \(diagonal^2=a^2+b^2=(3x)^2+(4x)^2\), and since \(diagonal=10\), then \(100=9x^2+16x^2\). Solving gives \(x=2\), hence \(a=3x=6\) and \(b=4x=8\). Therefore \(area=ab=6*8=48\). Sufficient.
Alternatively, even without calculating, one can observe that since the hypotenuse (diameter) is 10 and the legs are in the ratio of 3 to 4, then we have a 6-8-10 right triangle (Pythagorean Triple).
(2) The difference between the lengths of the rectangle's two adjacent sides is less than 3 centimeters.
Given that \(b-a \lt 3\). Square both sides: \(b^2-2ab+a^2 \lt 9\). Now, since \(diagonal=10^2=a^2+b^2\) then \(100-2ab \lt 9\), so \(ab \gt 45.5\). Therefore, \(area=ab \gt 45.5\), hence the area may or may not be more than 48. Not sufficient.
Answer: A
Is the area of a rectangle inscribed in a circle with a radius of 5 centimeters greater than 48 square centimeters?
Refer to the diagram below:
A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. Since a rectangle comprises two right triangles, a rectangle inscribed in a circle must have its diagonal as the diameter of the circle.
Given: \(radius=5\), hence \(diameter=diagonal=10\).
Question: \(area=ab=?\) (where \(a\) and \(b\) are the sides of the rectangle).
(1) The ratio of the lengths of the rectangle's sides is 3:4.
Given that \(\frac{a}{b}=\frac{3x}{4x}\), for some positive multiplier \(x\). Therefore, \(diagonal^2=a^2+b^2=(3x)^2+(4x)^2\), and since \(diagonal=10\), then \(100=9x^2+16x^2\). Solving gives \(x=2\), hence \(a=3x=6\) and \(b=4x=8\). Therefore \(area=ab=6*8=48\). Sufficient.
Alternatively, even without calculating, one can observe that since the hypotenuse (diameter) is 10 and the legs are in the ratio of 3 to 4, then we have a 6-8-10 right triangle (Pythagorean Triple).
(2) The difference between the lengths of the rectangle's two adjacent sides is less than 3 centimeters.
Given that \(b-a \lt 3\). Square both sides: \(b^2-2ab+a^2 \lt 9\). Now, since \(diagonal=10^2=a^2+b^2\) then \(100-2ab \lt 9\), so \(ab \gt 45.5\). Therefore, \(area=ab \gt 45.5\), hence the area may or may not be more than 48. Not sufficient.
Answer: A
General Discussion
21 Dec 2015, 15:15
Kudos
Bookmarks
i have doubt are there only 2 kinds of right angle triangle mentioned below or there can be other kinds of right angled triangle?
A right triangle where the angles are 30°, 60°, and 90°.
A right triangle where the angles are 45°, 45°, and 90°.
A right triangle where the angles are 30°, 60°, and 90°.
A right triangle where the angles are 45°, 45°, and 90°.
