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If RS = 2x, ST = 7x, and RT = 9, what is the length of ST? Simplify your answer and express it as a proper fraction or mixed number.

User Morad
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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.

User Abhink
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