Final answer:
To determine if a set of measurements could represent the side lengths of a triangle, we need to check if the sum of the two smaller sides is greater than the length of the longest side.
Step-by-step explanation:
To determine if a set of measurements could represent the side lengths of a triangle, we need to check if the sum of the two smaller sides is greater than the length of the longest side. Let's analyze each option:
A. 4 inches, 14 inches, 18 inches: 4 + 14 = 18, which is equal to the length of the longest side. This does not satisfy the triangle inequality theorem, so this set of measurements cannot represent the side lengths of a triangle.
B. 27 inches, 39 inches, 12 inches: 12 + 27 = 39, which is equal to the length of the longest side. This also does not satisfy the triangle inequality theorem, so this set of measurements cannot represent the side lengths of a triangle.
C. 8 inches, 8 inches, 20 inches: 8 + 8 = 16, which is less than the length of the longest side, 20 inches. This satisfies the triangle inequality theorem, so this set of measurements can represent the side lengths of a triangle.
D. 44 inches, 32 inches, 13 inches: 13 + 32 = 45, which is greater than the length of the longest side, 44 inches. This also satisfies the triangle inequality theorem, so this set of measurements can represent the side lengths of a triangle.
Therefore, the correct answer is option C (8 inches, 8 inches, 20 inches).