College

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 \ < \ x \ < \ 69[/tex]

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

C. [tex]11 \ < \ x \ < \ 69[/tex]

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

Answer :

To solve the problem, we use the triangle inequality theorem, which states that in any triangle with sides of lengths [tex]$a$[/tex], [tex]$b$[/tex], and [tex]$x$[/tex], the following must be true:

[tex]$$
|a - b| < x < a + b
$$[/tex]

Given that [tex]$a = 29$[/tex] and [tex]$b = 40$[/tex], we first calculate the absolute difference:

[tex]$$
|29 - 40| = 11
$$[/tex]

Next, we calculate the sum of these two sides:

[tex]$$
29 + 40 = 69
$$[/tex]

Thus, the inequality for the third side [tex]$x$[/tex] is:

[tex]$$
11 < x < 69
$$[/tex]

Among the provided choices, the inequality that correctly represents this range is:

Option C: [tex]$\; 11
Therefore, the correct answer is option C.

Other Questions