Question

1. two sides of a triangle measure 7 feet and 19 feet. if x is the length of the third side, which inequality shows the range of possible lengths for the third side?

a. 7 < x < 19
b. 12 < x < 26
c. 19 < x < 26
d. 7 < x < 12

Explanation:

Step1: Recall Triangle Inequality Theorem

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. For a triangle with sides \( a \), \( b \), and \( x \), we have three inequalities: \( a + b>x \), \( a + x>b \), and \( b + x>a \). However, for the range of the third side \( x \) (given two sides \( a = 7 \) and \( b = 19 \)), we can simplify it to \( |a - b|

Step2: Calculate the difference and sum of the two sides

First, find the difference between the two given sides: \( 19 - 7=12 \). Then, find the sum of the two given sides: \( 19 + 7 = 26 \).

Step3: Determine the inequality for \( x \)

Using the triangle inequality theorem, the length of the third side \( x \) must be greater than the difference of the other two sides and less than the sum of the other two sides. So, \( 12

Answer:

B. \( 12 < x < 26 \)