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 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
11 Aug 2025, 09:09
Kudos
Bookmarks
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:
100% (01:33) correct
0% (00:00) wrong based on 1 sessions
History
Date
Time
Result
Not Attempted Yet
The area of the circle above, with center C, is \(36π\), and \(x > 90.\)
Quantity A
The area of the triangle
Quantity B
18
Attachment:
GMAT-Club-Forum-egkjlcow.png [ 13.42 KiB | Viewed 143 times ]
24 Aug 2025, 05:31
Kudos
Bookmarks
Official Explanation
Use the formula for the area of a circle, area = \(πr^2.\) Since the area is given as \(36π,\) we know \(πr^2 = 36π.\) Now look for cancellation! Dividing both sides by \(π\) yields \(r^2 = 36\) and \(r = 6.\) Because the radius is 6, two sides lengths of the triangle equal 6. If x were equal to 90, then the triangle would be a right triangle and its area, given by × base × height would equal × 6 × 6, or 18.
But we are given x > 90, which makes the height of the triangle less than 6 and the area less than 18, so (B) is greater. Notice that in an obtuse triangle, when the base is a side adjacent to the obtuse angle, then the altitude drawn for the purposes of computing area lies outside the triangle and is smaller than either of the other two sides.
Answer: B
Use the formula for the area of a circle, area = \(πr^2.\) Since the area is given as \(36π,\) we know \(πr^2 = 36π.\) Now look for cancellation! Dividing both sides by \(π\) yields \(r^2 = 36\) and \(r = 6.\) Because the radius is 6, two sides lengths of the triangle equal 6. If x were equal to 90, then the triangle would be a right triangle and its area, given by × base × height would equal × 6 × 6, or 18.
But we are given x > 90, which makes the height of the triangle less than 6 and the area less than 18, so (B) is greater. Notice that in an obtuse triangle, when the base is a side adjacent to the obtuse angle, then the altitude drawn for the purposes of computing area lies outside the triangle and is smaller than either of the other two sides.
Answer: B
