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, can be represented by the inequality 4 < x < 20, which is Option A.
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. This theorem states that the length of any side of a triangle must be greater than the difference between the other two sides and less than the sum of the other two sides. If we call the third side x, to satisfy the Triangle Inequality Theorem, x must be greater than the difference of 12 and 8, and less than their sum. Therefore, we have: x > 12 - 8, x < 12 + 8. By simplifying the inequalities, we get x > 4, and x < 20. So the range of possible values for x is 4 < x < 20. Option A, 4 < x < 20, is the correct inequality representing the range of possible values for x in this scenario.