Question

if rs = x + 6, st = 9x, and rt = 16, 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 have the equation $(x + 6)+9x=16$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $x+9x + 6=16$, which simplifies to $10x+6 = 16$.

Step3: Solve for $x$

Subtract 6 from both sides: $10x=16 - 6$, so $10x=10$. Then divide both sides by 10, we get $x = 1$.

Step4: Find the value of $ST$

Since $ST = 9x$ and $x = 1$, then $ST=9\times1=9$.

Answer:

9