Which of the following CANNOT be the lengths of the sides of a triangle?
What type of question are we asked to answer?
This is a CANNOT BE question – that is the information in the answer contradicts a fact we should know.
What is the topic? we are dealing with a geometry problem, in particular triangles.
This is a question regarding sides of a triangle. At this point the sentence that states that the combined length of each pair of sides should be greater than the third side of the triangle should surface somewhere in your mind. This actually make sense – if you imagine the longest side as a line to which the two other sides are connected at the ends, and these two shorter sides are trying to meet one another – their sum should be greater than that of the longest side. It is clear that 1, 2, 4 is a set of lengths that does not do that since 1+2=3<4 and thus this triangle can’t close.