Question

A triangle has side lengths of 18 & 13. Which of the following could not be a measure of the third side?
Question 9 options:
1) 4
2) 30
3) 22
4) 5

Answer 1

I have a nice rule for this... if you're given two sides a and b of a triangle, then the length of the third side must fall in this interval...
\[\large \left(|a-b| \quad , \quad a+b\right)\]
Note the open intervals :D

Answer 2

So, in this case, a is 18
b is 13

So the length of the third side must fall between 18 - 13, which is 5
and 18+13 which is 31

Note that 5 and 31 themselves may not be a length of the third side, it must be strictly between those two values.