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.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
If the Area of a Triangle ABC is given by the formula [#permalink]
14 Oct 2012, 20:45
1
This post received KUDOS
2
This post was BOOKMARKED
00:00
A
B
C
D
E
Difficulty:
(N/A)
Question Stats:
100% (01:42) correct
0% (00:00) wrong based on 29 sessions
If the Area of a Triangle ABC is given by the formula 1/4 (a^2 + b^2), where a and b are the lengths of the two sides, then the angles of the triangle are?
A) 30, 60, 90 B) 60,40,80 C) 60,60,60 D) 90,45,45 E) None of the above _________________
"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas
Last edited by vomhorizon on 15 Oct 2012, 01:49, edited 1 time in total.
Re: If the Area of a Triangle ABC is given by the formula [#permalink]
15 Oct 2012, 00:46
1
This post received KUDOS
vomhorizon wrote:
If the Area of a Triangle ABC is given by the formula 1/4 (a^2 + b^2), where a and b are the lengths of the two sides, then the angles of the triangle are?
A) 30, 60, 90 B) 60,40,80 C) 60,60,60 D) 90,45,45 E) None of the above
The answer cannot be C: in this case, the triangle would be equilateral, so necessarily \(a = b.\) Then \(\frac{a^2+b^2}{4}=\frac{2a^2}{4}\) while the area of the triangle would be \(\frac{\sqrt{3}a^2}{4}.\) The two expressions are equal only if \(a=0.\) _________________
PhD in Applied Mathematics Love GMAT Quant questions and running.
Re: If the Area of a Triangle ABC is given by the formula [#permalink]
15 Oct 2012, 00:55
1
This post received KUDOS
vomhorizon wrote:
If the Area of a Triangle ABC is given by the formula 1/4 (a^2 + b^2), where a and b are the lengths of the two sides, then the angles of the triangle are?
A) 30, 60, 90 B) 60,40,80 C) 60,60,60 D) 90,45,45 E) None of the above
We can eliminate answer B, as on the GMAT we don't have any means to test it.
If the triangle is a right triangle, then \(a\) and \(b\) can be its two legs, or one is a leg and the other one is the hypotenuse. It is easier to test the case when \(a\) and \(b\) are legs.
If the triangle is a right triangle with its two legs \(a\) and \(b\), then \(a^2+b^2\) is the square of the diameter of the circle in which this triangle is inscribed. \(\frac{a^2+b^2}{4}\) represents half of the area of the square inscribed in the same circle. Recall the formula for the area of a square being half of the diagonal squared, which in this case is \(\frac{a^2+b^2}{2}\). It follows that the triangle is an isosceles right triangle.
There is just one correct answer (this is a PS question), so we should stop checking other options. A cannot be the answer, in the expression for the area of the triangle, a factor of \(\sqrt{3}\) would necessarily appear (try to work out the two cases), but on the test, we should stop after finding the correct answer rather then continue to prove that the other options are not acceptable.
Answer D. _________________
PhD in Applied Mathematics Love GMAT Quant questions and running.
Re: If the Area of a Triangle ABC is given by the formula [#permalink]
18 Dec 2012, 03:10
I did it in this way. Not able to figure out. I was able to rule out all the other options. How is it D? Here is what i did.
Now the question says that two sides are a and b, it doesnt talk about the 3rd side. In case of option D Case 1(a,b,c) here let a = b and c be the hypotenuse ar = (1/2)base×height = (1/2)ab = (1/2)a² area from the equation = (1/4)(a² + b²) = (1/4)(2a²) = (1/2)a² both are equal
Case 2 (a,a,b) so a² + a² = b² = 2a² ar = (1/2)base×height = a²/2 ar from the equation = (1/4)(a² + b²) = (1/4)(a² + 2a²) = (3/4)a² the above two are not equal.
Re: If the Area of a Triangle ABC is given by the formula [#permalink]
26 Dec 2013, 14:26
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Perhaps known best for its men’s basketball team – winners of five national championships, including last year’s – Duke University is also home to an elite full-time MBA...
Hilary Term has only started and we can feel the heat already. The two weeks have been packed with activities and submissions, giving a peek into what will follow...