Final answer:
Only Option C (12 inches, 18 inches, 7 inches) satisfies the Triangle Inequality Theorem, where the sum of the two shorter sides is greater than the third side, thus it is the only set that can form a triangle.
Step-by-step explanation:
The question asks which set of three measures could form a triangle. To determine if three lengths can form a triangle, you can use 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. We can apply this theorem to each of the given options.
- Option A: 27 yards, 65 yards, 38 yards - To check this, we add the two shortest lengths and see if the sum is greater than the longest length. 27 yards + 38 yards = 65 yards. Since the sum equals the longest side, they cannot form a triangle.
- Option B: 150 meters, 35 meters, 65 meters - Again, adding the two shorter lengths: 35 meters + 65 meters = 100 meters, which is less than the longest side, so these lengths also do not form a triangle.
- Option C: 12 inches, 18 inches, 7 inches - The sum of the two shorter lengths is 12 inches + 7 inches = 19 inches. This sum is greater than the third side (18 inches), so these lengths could form a triangle.
- Option D: 44 feet, 38 feet, 98 feet - The sum of the two shorter sides is 44 feet + 38 feet = 82 feet, which is less than the longest side. So, these lengths cannot form a triangle.
Based on these checks, Option C is the only set of measures that satisfies the Triangle Inequality Theorem and can form a triangle.