Final answer:
Triangle B, with sides measuring 3, 4, and 5, is a multiple of a triangle with sides x, x-5, and x+5, fulfilling the Pythagorean theorem and maintaining the proportional relationship of the sides when x is greater than 0.
Step-by-step explanation:
The triangle is a scalar multiple of a triangle with sides x, x-5, and x+5, assuming that x is greater than 0. To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (s) is equal to the sum of the squares of the lengths of the other two sides (D and L). To find a triangle that is a multiple of the original, we must look for figures where the sides follow this same relationship and are simple multiples of the original side lengths.
Among the options provided, only triangle B with sides measuring 3, 4, and 5 satisfies both the Pythagorean theorem (3²+4² = 5²) and is a multiple of a triangle described by the aforementioned relationship. If we set x to 5, we get sides 5, 10, and 15, which when divided by 5 result in sides 1, 2, and 3. Each side of triangle B (3, 4, 5) is exactly 3 times the respective sides when x = 5, which indicates that triangle B is indeed a multiple of the triangle with sides x, x-5, and x+5 where x is greater than 0.