Question

s is the mid - point of rt. if st = 7x and rt = 8x + 6, what is rt? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since \(S\) is the mid - point of \(\overline{RT}\), then \(RS = ST\) and \(RT=RS + ST\), so \(RT = 2ST\).

Step2: Set up equation

We know that \(ST = 7x\) and \(RT=8x + 6\), and \(RT = 2ST\). Substitute \(ST = 7x\) into \(RT = 2ST\), we get \(8x+6=2\times7x\).

Step3: Solve the equation for \(x\)

\[

$$\begin{align*} 8x + 6&=14x\\ 6&=14x-8x\\ 6&=6x\\ x& = 1 \end{align*}$$

\]

Step4: Find the value of \(RT\)

Substitute \(x = 1\) into the expression for \(RT\). Since \(RT=8x + 6\), then \(RT=8\times1+6=14\).

Answer:

14