Final answer:
The correct answer is option B: 18, 24, 30, as they adhere to the Pythagorean theorem and maintain the same ratio as the given triangle ABC.
Step-by-step explanation:
Right triangle ABC is similar to right triangle DEF. The side lengths for triangle ABC are 15, 20, and 25, respectively, which means triangle DEF must have sides in the same ratio. To determine which values could represent the side lengths of triangle DEF, we must ensure that the sides follow the Pythagorean theorem which states that in a right triangle the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, which can be written as a² + b² = c².
Given option B, the sides are 18, 24, and 30. Applying the Pythagorean theorem: 18² + 24² = 324 + 576 = 900, which is indeed 30². So, these values follow the same 3:4:5 ratio and also adhere to the Pythagorean theorem, making option B correct.