Final answer:
To determine the length of ST when RS = 2x, ST = 7x, and RT = 9, we derive the value of x from the equation 2x + 7x = 9 and find that ST = 7.
Step-by-step explanation:
To find the length of ST, we must understand that RS + ST equals RT because RS and ST are parts of segment RT. With the given equations RS = 2x, ST = 7x, and RT = 9, we combine RS and ST to form the equation 2x + 7x = 9. This simplifies to 9x = 9.
Simplify the equation. By dividing both sides by 9, we find that x = 1. We then substitute back into the equation for ST: ST = 7x = 7(1) = 7.
Now we have the length of ST as 7. Since there are no units given, we don't attach a specific unit to the answer.