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

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

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