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Which of the following could be the sides of an obtuse...

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Which of the following could be the sides of an obtuse...

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Which of the following could be the sides of an obtuse angle triangle?

I. 1, 2, 3
II. 2, 3, 4
III. 2, 3, 5

A. I and III only
B. II only
C. III only
D. I and II only
E. I, II and III

The OA is B.

I don't have clear this PS question, why II only? I appreciate if any expert explain it for me. Thank you so much.

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AAPL wrote:
Which of the following could be the sides of an obtuse angle triangle?

I. 1, 2, 3
II. 2, 3, 4
III. 2, 3, 5

A. I and III only
B. II only
C. III only
D. I and II only
E. I, II and III

The OA is B.

I don't have clear this PS question, why II only? I appreciate if any expert explain it for me. Thank you so much.
This question is an application of the "third side" rule of triangles: The third side of a triangle must be less than the sum of the other two sides and it must be greater than the difference of the other two sides.

(Algebraically: If you have a triangle with sides x, y, and z, we know that x < y + z and x > y - z.)

First statement: 1, 2, 3 - this violates the third side rule, as 3 is not less than 1 + 2. If the third side is not less than the sum of the other two sides, then we don't have a triangle. This is out.
Third statement: 2, 3, 5 - this violates the third side rule, as 5 is not less than 2 + 3. If the third side is not less than the sum of the other two sides, then we don't have a triangle. This is out.

If we eliminate I and III, we're left with II. The answer is B

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