Final answer:
The minimum and maximum side lengths of the third side of a triangle with side lengths 9 inches and 14 inches are 5 inches and 23 inches respectively.
Step-by-step explanation:
To find the minimum and maximum side lengths of the third side of a triangle, we can apply the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, for the minimum side length, we subtract the known side lengths: 14 - 9 = 5 inches. And for the maximum side length, we add the known side lengths: 14 + 9 = 23 inches. Therefore, the minimum side length is 5 inches and the maximum side length is 23 inches.
Learn more about Triangle Inequality Theorem