Final answer:
To determine which set of side lengths form a right triangle, use the Pythagorean theorem. Only the set of side lengths 3 ft, 6 ft, 5 ft forms a right triangle.
Step-by-step explanation:
To determine which set of side lengths form a right triangle, we can use the Pythagorean theorem. According to the Pythagorean theorem, in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (hypotenuse). Let's check each set of side lengths:
- 50 in., 48 in., 14 in.: Not a right triangle. (50^2 + 48^2 ≠ 14^2)
- 53 m, 48 m, 24 m: Not a right triangle. (53^2 + 48^2 ≠ 24^2)
- 3 ft, 6 ft, 5 ft: Forms a right triangle. (3^2 + 6^2 = 5^2)
- 8 cm, 17 cm, 14 cm: Not a right triangle. (8^2 + 17^2 ≠ 14^2)