$S$ is the midpoint of $\overline{R T}$. If $S T=x+6$ and $R T=3 x+6$, what is $S T$ ?
Simplify your answer and write it as a proper fraction, mixed number, or integer.
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Answer

So, the final answer is $S T = \boxed{12}$.

Steps

Step 1 ：Given that S is the midpoint of RT, it means that ST = SR.

Step 2 ：We know that ST = x + 6 and RT = 3x + 6.

Step 3 ：Since RT = SR + ST, we can substitute the values of ST and RT into the equation and solve for x.

Step 4 ：We get the equation $3x + 6 = 2x + 12$.

Step 5 ：Solving this equation, we find that x = 6.

Step 6 ：Substituting x = 6 back into the equation for ST, we find that ST = 12.

Step 7 ：So, the final answer is $S T = \boxed{12}$.