Which of the following could be the sides of an obtuse angled triangle

This question would have been difficult if one of the answer choices had option of NONE.

1 and 3 are out as they are not even eligible for any triangle, as sum of two sides should always be greater than the third.

For obtuse angle the sum of squares of two sides should be less than square of the third.

since \(4^2 > 3^2 + 2^2\) this triangle has one obtuse angle.

that's a typo.. I have corrected.

yeah..As all of you have pointed out two of the options are straightaway out because they are not even triangles..I was looking after rule for obtuse triangle which Gurpreet has mentioned rightly.

Thankyou all.

For obtuse angle the sum of squares of two sides should be less than square of the third. - had forgotten about this rule. Thanks Gurpreet

What is obtuse triangle? I answered the question by applying the third-side of the triangle rule.

1,2 - the third side should be 1 < x < 3 HENCE we eliminate A,D and E
2,3 - the third side should be 1 < x < 5 HENCE we eliminate C

We are left with B. Let's double check,
2,3 - the third side should be 1 < x < 5 HENCE 4 is correct

HENCE, (B)

good question.Lesson learnt about obtuse triangle.
B it is.

Which of the following could be the sides of an obtuse angled triangle?
1, 2, 3
2, 3, 4
2, 3, 5



A. I and III only

B. II only

C. III only

D. I and II only

E. I, II and III

For any triangle with sides a,b,c, the following rules for sides MUST be followed:

|a-b| \(<\) c \(<\) a+b (this has to be true for ALL the sides!)


This relation is not followed by triangles (1,2,3) and (2,3,5) when 3=2+1 and 5=2+3.

Thus, the only case possible is Case II , hence B is the correct answer.

Hi hiteshahire22,

This rule that this question is built around is called the Triangle Inequality Theorem; Engr2012 has explained the math behind the rule well-enough that I won't rehash it, but I can provide some background. In real simple terms, if you take ANY 2 sides of a triangle, then they should sum to a total that is GREATER than the third side (and that relationship MUST exist when you choose ANY pair sides).

It's a rare geometry rule that you're more likely to see on Test Day if you're doing well in the Quant section (although you could do well and NOT see it, the Theorem can sometimes be "hidden" behind other concepts so you should keep your eyes open for it). You can actually use this rule to figure out minimum/maximum area or minimum/maximum perimeter of a triangle as well.

GMAT assassins aren't born, they're made,
Rich

Here triangles in the statements are not possible as they do not satisfy the property that => sum of two sides must be greater than the third side => it cannot be equal to the third side

A rule I had completely forgotten.!!! Could you please share more tips and tricks like this??

In order to be side lengths of a triangle, the triangle inequality tells us that the sum of the two shortest sides is greater than the longest side. In this case, we see that only II (2, 3, 4) are the side lengths of a triangle. Since no answer choice is “None” or “None of these,” we can safely say B must be the correct answer without going further to show that the 3 side lengths are indeed the sides of an obtuse angle triangle.

Note: While we have already determined that the answer is B, if we really want to verify that the triangle with sides 2, 3, and 4 is an obtuse triangle, we need the following fact: If c is the longest side in a triangle and a^2 + b^2 < c^2, then the triangle is an obtuse triangle. Since the numbers given to us satisfy 2^2 + 3^2 < 4^2, this triangle is indeed an obtuse triangle.

Answer: B

Asked: Which of the following could be the sides of an obtuse angled triangle?

I. 1, 2, 3
1+2=3
Triangle is not possible

II. 2, 3, 4
4^2>2^2+3^2
Is a triangle with obtuse angle

III. 2, 3, 5
2+3=5
Not a triangle

IMO B

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For a triangle to be obtuse triangle, a^2> b^2+c^2

I. 1, 2, 3 => This is not a triangle since 3 = 2+1 => not satisfies the property of sides of a triangle
II. 2, 3, 4 => 4^2 > 2^2 + 3^2 => 16>4+9 => 16>13 Satisfies
III. 2, 3, 5 => This is not a triangle since 5 = 2+3 => not satisfies the property of sides of a triangle

Hence B