Final answer:
None of the given options (24 inches, 28 inches, 30 inches, 32 inches) satisfy the Triangle Inequality Theorem for the third side of a triangle with the other two sides measuring 12 inches and 15 inches, thus none are possible measurements for the third side.
Step-by-step explanation:
The third side of a triangle must comply with the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. With given side lengths of 12 inches and 15 inches, let's evaluate the possible measurement of the third side:
- For option (a) 24 inches, 12 + 15 > 24 and 15 + 24 > 12, but 12 + 24 is not greater than 15, so this does not satisfy the Triangle Inequality Theorem.
- For option (b) 28 inches, 12 + 15 is not greater than 28, so this fails the theorem.
- For option (c) 30 inches, 12 + 15 is equal to 27 which is not greater than 30, thus failing the theorem.
- For option (d) 32 inches, 12 + 15 is less than 32, which fails the theorem.
Therefore, none of the provided options are possible measurements for the third side of the triangle.