Question

If two sides of a triangle measure 9cm and 23cm which could be the measure of the third side of a triangle?

Answer 1

23cm. If the remaining side were 9cms in length, it wouldn't be long enough to connect the other two sides.

Answer 2

rule:
longest side has to be less than the sum of the other 2 sides

if we assume that 23 is longest
9+?≤23
minus 9 both sides
?≤14

if we assume that 23 is not the longest
9+23≤?
32≤?


BUT

the triangle changes
and the longest side is changing because when one becomes shorter, there is a new longest

so therefor the legnth is any number from 14 to 32, not including 14 or 32