Is the triangle ABC with sides a,b,c a right-angled triangle?

Nice observation

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
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The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

\(a^2 + c^2 < b^2\) from condition 2) means the angle B is greater than 180° and the triangle ABC is obtuse.
No obtuse triangle has a right interior angle and we have an answer 'no'

Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, condition 2) is sufficient.


Condition 1)

IF \(a = 3, b = 5, c = 4\), then the triangle is a right triangle and the answer is 'yes'.
If \(a = b = c = 1\), the triangle is not a right triangle and the answer is 'no'

Since condition 1) does not yield a unique solution, it is not sufficient.

Therefore, B is the answer.

The question is very tricky and full of traps.