Given:
Two sides of a triangle are 9 and 5.
To find:
The range of possible measures for the third side.
Solution:
In a triangle, the sum of smaller sides must be greater than the largest side.
Let x be the measure of third side.
Case 1: When x is the largest side, then
[tex]9+5>x[/tex]
[tex]14>x[/tex] ...(i)
Case 2: When 9 is the largest side, then
[tex]x+5>9[/tex]
[tex]x>9-5[/tex]
[tex]x>4[/tex] ...(ii)
Using (i) and (ii), we get
[tex]4<x<14[/tex]
Therefore, the range of possible measures for the third side is [tex]4<x<14[/tex].
