Hi
If \(a^2+b^2 < c^2\),
it means the angle between side a & b is obtuse, the triangle is obtuse.
If \(a^2+b^2 > c^2\),
it means the angle between a & b is acute, but since other angle can be obtuse, the triangle cant be taken as acute.If \(a^2+b^2 =c^2\),
it means the angle between a & b is 90 deg, hence the triangle is right.
I hope it helps.
ENGRTOMBA2018 wrote:
Hi Engr2012,
The problem I had with the question was that no where in the question stem does it mention that variables a,b, and c represent the lengths of triangle ABC. So I thought that If I had to assume that a,b,c represent the lengths of a triangle, then I can also assume that length c of triangle of ABC was the biggest as it is when describing the Pythagorean theorem. I agree that the official answer is E because we don't know whether C represents the largest side of the triangle or not.
Your interpretation is partially correct. Even if you know c is the largest side, I gave you 2 cases above that make statement 1 as not sufficient.
So in order to answer this particular question, the knowledge of whether side c is the largest is not important.
Hope this helps.[/quote]
In your example, the sides of the triangle were 3,4, and 6. If we were to assume that side c was the largest side of the triangle, then your example doesn't satisfy statement 1.
Let's say a=3, b=4, and c=6 then \(a^2 +b^2 <c^2\)
I would expect it to be obtuse triangle.
According to GMAT expert, Mike Mcgarry of
Magoosh, the following properties are true if c is the largest side:
If \(a^2+b^2 < c^2\), the triangle is obtuse.
If \(a^2+b^2 > c^2\), the triangle is acute.
If \(a^2+b^2 =c^2\), the triangle is right.
Here is a link to the article:
https://magoosh.com/gmat/2012/re-thinkin ... le-obtuse/[/quote]
I dont think I made myself clear. What I wanted to say with my example above, with sides 3,4,6, until the question tells me that c=largest side, I can play around with the sides to prove that a statement may or may not work. A "sufficient" statement MUST work for ALL different cases possible within scope of the question and the given statement(s).
(3,4,6) does work as an example case for statement 1. You are given a^2+b^2>c^2. No one knows whether c is the greatest side. I can take c=3 or 4 or 6 in this case to prove my point. This ambiguity is what is making this statement not sufficient.
Isnt 6^2+4^2>3^2? Yes. Can you have a triangle with sides 3,4,6 ? Yes.
As per the definition, yes a^2+b^2>c^2 will give you an acute angled triangle only if you know that c is the greatest side. You can not apply this in this question because of the inherent ambiguity.Hope this clears the confusion.
Additionally, I have updated my post above.[/quote]
_________________