Question

point s is on line segment \\(\overrightarrow{rt}\\). given \\(rt = 3x\\), \\(rs = 3x - 5\\), and \\(st = 3x - 1\\), determine the numerical length of \\(\overline{rt}\\).

Explanation:

Step1: Use segment addition postulate

Since \( S \) is on \( \overline{RT} \), we have \( RS + ST = RT \). Substituting the given expressions: \( (3x - 5) + (3x - 1) = 3x \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 6x - 6 = 3x \). Subtract \( 3x \) from both sides: \( 3x - 6 = 0 \). Add 6 to both sides: \( 3x = 6 \). Divide by 3: \( x = 2 \).

Step3: Find length of \( RT \)

Substitute \( x = 2 \) into \( RT = 3x \): \( RT = 3(2) = 6 \).

Answer:

6