Final answer:
Similar triangles have proportional sides, so for triangle NOP with side lengths 5 cm, 7 cm, and 9 cm to be similar to triangle RST, the sides of RST must be multiples of these lengths while keeping the same ratio.
Step-by-step explanation:
The question involves the concept of similar triangles in Geometry. Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional in length. In the case of triangle NOP with sides 5 cm, 7 cm, and 9 cm being similar to triangle RST, the side lengths of RST must be in the same ratio as NOP. This means we can multiply each side of NOP by the same positive number (other than 1) to find possible side lengths for RST. For example, if we multiply each side by 2, the sides of RST would be 10 cm, 14 cm, and 18 cm. It's crucial to maintain the ratio between the sides to ensure the triangles remain similar.