Question

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. -11 < x < 69
b. 11 ≤ x ≤ 69
c. 11 < x < 69
d. -11 ≤ x ≤ 69

Explanation:

Step1: Recall triangle inequality theorem

For any triangle with side lengths $a$, $b$, $c$, the sum of any two sides must be greater than the third side. Let the third side be $x$.

Step2: Set up first inequality

The sum of the two given sides must be greater than $x$:
$29 + 40 > x$
$69 > x$

Step3: Set up second inequality

The sum of the third side and the shorter given side must be greater than the longer given side:
$x + 29 > 40$
$x > 40 - 29$
$x > 11$

Step4: Combine inequalities

Since side length cannot be negative or zero, we only consider the valid positive range from the two inequalities.

Answer:

C. $11< x< 69$