Question

s is the midpoint of \\(overline{rt}\\). if \\(rs = 6x\\) and \\(st = x + 5\\), what is \\(rs\\)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use midpoint property

Since \( S \) is the midpoint of \( \overline{RT} \), \( RS = ST \). So we set up the equation \( 6x = x + 5 \).

Step2: Solve for \( x \)

Subtract \( x \) from both sides: \( 6x - x = x + 5 - x \), which simplifies to \( 5x = 5 \). Then divide both sides by 5: \( \frac{5x}{5} = \frac{5}{5} \), so \( x = 1 \).

Step3: Find \( RS \)

We know \( RS = 6x \), substitute \( x = 1 \): \( RS = 6\times1 = 6 \).

Answer:

\( 6 \)