Question

if rs = 6, st = 6x, and rt = 9x, what is st? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $RT=RS + ST$, we substitute the given values: $9x=6 + 6x$.

Step2: Solve for $x$

Subtract $6x$ from both sides of the equation: $9x-6x=6+6x - 6x$, which simplifies to $3x = 6$. Then divide both sides by 3: $x=\frac{6}{3}=2$.

Step3: Find the value of $ST$

We know that $ST = 6x$. Substitute $x = 2$ into the equation for $ST$, so $ST=6\times2 = 12$.

Answer:

12