Final answer:
The range of possible values for the third side of a triangle with sides measuring 8 inches and 12 inches, according to the Triangle Inequality Theorem, is 4 < x < 20 inches. Therefore, the correct option is C. 4 < x < 20.
Step-by-step explanation:
To determine the range of possible values for the third side of a triangle with sides measuring 8 inches and 12 inches, we use the Triangle Inequality Theorem. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Following this rule, we can set up two inequalities:
- 8 + 12 > x (The sum of the two given sides must be greater than the third side.)
- 8 + x > 12 and 12 + x > 8 (The sum of each given side and the unknown side must be greater than the other given side.)
The first inequality simplifies to 20 > x, meaning that the value of the third side must be less than 20 inches. Our second set of inequalities simplify to x > 4 (from 12 - 8) and x > -4 (from the third side not possible to be negative, we ignore this). Therefore, combining these inequalities, we get 4 < x < 20, which means that the third side must be greater than 4 inches but less than 20 inches.
The correct answer is C. 4 < x < 20.