Final answer:
Side lengths of triangle Z are a scaled version of triangle M, following a specific ratio or scale factor. In right triangles, these lengths should also adhere to the Pythagorean theorem.
Step-by-step explanation:
The question pertains to the concept of similar triangles in mathematics. In similar triangles, corresponding sides are proportional. This means that each side of triangle Z should be a scaled version of the corresponding side of triangle M. That is, if the scale factor is k, and the side lengths of triangle M are a, b, and c, then the side lengths of triangle Z will be ka, kb, and kc. Using trigonometry and the Pythagorean theorem, one can also find relationships between the sides of right triangles. Whenever provided with side lengths, they must conform with the Pythagorean theorem if the triangle is a right triangle, and the ratios between the sides must remain consistent for similar triangles.
To determine the possible side lengths of triangle Z, we need to consider that triangle Z is a scaled copy of triangle M. This means that the corresponding sides of Z and M are proportional, meaning they have the same ratio.
For example, if triangle M has side lengths of 4, 6, and 8, and triangle Z is a scaled copy of M, then the corresponding side lengths of Z would be 2, 3, and 4 because they have the same ratio (2:4 = 3:6 = 4:8).
Therefore, any set of side lengths that have the same ratio as the corresponding sides of triangle M could be the side lengths of triangle Z.