How to figure out this question: Which of the following could be the lengths of the sides of a triangle?

the options are a) 2, 3 and 1 b) 3, 6 and 9 c) 3, 10 and 6 d) 4, 7 and 2 e) 7, 8 and 9





apparently the answer is e, but how do you figure it out? what are the rules to figure out if the three numbers can make a triangle?How to figure out this question: Which of the following could be the lengths of the sides of a triangle?
The triangle rules state that the sum of the two shortest sides must be longer than the longest side. It's only in e) that this is the case.





Look at d) for example. One side is 7. There is no way the 4 and the 2 can meet to close the triangle. Draw it yourself and see.How to figure out this question: Which of the following could be the lengths of the sides of a triangle?
try to draw the triangle or add the sides 2 at a time


no 2 sides can add up to the third or less


a) 1,2,3 this is a line of length 3


b) 3,6,9 same, length 9


c) 3,10,6 .... 3 and 6 together will not meet the 10 side on both ends


d) same as c



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I'm doing the PSAT practice test as well, and this gives explanations to every problem. I'm using it for the one's I can't figure out