Two sides of a triangle have the following measures. Find the range of possible measures for the third. (Two sides given are 9 and 5.)

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

           ...(i)

Case 2: When 9 is the largest side, then

           ...(ii)

Using (i) and (ii), we get

Therefore, the range of possible measures for the third side is .