Select the correct answer.

A triangle has one side of length 29 units and another of length 40 units. Determine the range in which the length of the third side must lie.

A. [tex]$-11\ \textless \ x\ \textless \ 69$[/tex]

B. [tex]$11 \leq x \leq 69$[/tex]

C. [tex]$11\ \textless \ x\ \textless \ 69$[/tex]

D. [tex]$-11 \leq x \leq 69$[/tex]

To determine the possible length of the third side of a triangle when two sides are given, we use the triangle inequality. The triangle inequality states that the length of any side must be less than the sum of the other two sides and greater than the absolute difference of the other two sides.

Let the given sides be [tex]$29$[/tex] and [tex]$40$[/tex], and let the third side be [tex]$x$[/tex]. Then:

1. The third side must be less than the sum of the two sides:
[tex]$$
x < 29 + 40 = 69
$$[/tex]

2. The third side must be greater than the absolute difference of the two sides:
[tex]$$
x > \left|29 - 40\right| = 11
$$[/tex]

Thus, combining these two inequalities, we have:
[tex]$$
11 < x < 69
$$[/tex]

This corresponds to option C.