Question

s is the midpoint of $overline{rt}$. if $rs = 9x$ and $st = x + 8$, what is $rs$?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

Since S is the mid - point of $\overline{RT}$, then $RS = ST$. So, $9x=x + 8$.

Step2: Solve for x

Subtract x from both sides: $9x−x=x + 8−x$, which simplifies to $8x=8$. Then divide both sides by 8: $x = 1$.

Step3: Find RS

Substitute $x = 1$ into the expression for RS. Since $RS = 9x$, then $RS=9\times1=9$.

Answer:

9