Final answer:
Only one set of side lengths, option (d) 20, 14, shows a ratio that is potentially similar to triangle ABC if it maintains the same ratio of side lengths and could form a right triangle in accordance with the Pythagorean theorem. This assumes triangle ABC is also a right triangle with proportional sides.
Step-by-step explanation:
The question asks which set of side lengths can form a triangle similar to triangle ABC. To determine similarity, the side lengths must be proportional to those of triangle ABC. To check for similarity using side lengths alone, you can either know the side lengths of triangle ABC or use the Pythagorean theorem if it's a right triangle. As triangle ABC's side lengths aren't provided, we'll focus on solutions using Pythagorean theorem where applicable.
For option (a) 10, 7, choice (d) 20, 14 and choice (g) 17, 20, 25 are potential candidates as their ratios match. Specifically, choice (d) 20, 14 has side lengths that maintain the same 10:7 ratio as choice (a). The Pythagorean theorem, which states that in a right triangle labeled a and b as the legs and c as the hypotenuse, can be written as a² + b² = c², suggests these dimensions could form right triangles. Applying the theorem to option (d), we find it satisfies the condition 14² + 20² = 21², thus confirming a right triangle. Therefore, option (d) can form a triangle similar to ABC if ABC is also a right triangle with sides proportional to 14 and 20.