Final answer:
Only Option D, with measurements of 80 in, 20 in, and 100 in, satisfies the Pythagorean theorem and could represent the side lengths of a right triangle.
Step-by-step explanation:
The subject at hand is determining which set of given measurements could represent the side lengths of a right triangle. To verify whether a set of three numbers can form a right triangle, we utilize the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. If the numbers satisfy the equation c² = a² + b², where 'c' is the longest side, then they can be the side lengths of a right triangle.
Step-by-Step Analysis
- Option A: For 2140 in, 60 in, 70 in, checking if 2140² = 60² + 70² does not hold since 4579600 (+) 4200 + 4900.
- Option B: For 190 in, 160 in, 160 in, since the lengths are not distinct, this cannot be a right triangle.
- Option C: For 110 in, 20 in, 100 in, checking if 110² = 20² + 100² does not hold since 12100 (+) 400 + 10000.
- Option D: For 80 in, 20 in, 100 in, checking if 100² = 80² + 20² holds since 10000 = 6400 + 400.
Only Option D satisfies the Pythagorean theorem, and hence it is the correct choice for the side lengths of a right triangle.