Question

on a line segment, s is between r and t. if rs = 9x, st = x + 14, and rt = 12x + 8, what is rs? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

Since \( S \) is between \( R \) and \( T \), we have \( RS + ST = RT \). Substituting the given expressions: \( 9x + (x + 14) = 12x + 8 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 10x + 14 = 12x + 8 \). Subtract \( 10x \) from both sides: \( 14 = 2x + 8 \). Subtract 8 from both sides: \( 6 = 2x \). Divide by 2: \( x = 3 \).

Step3: Find \( RS \)

Substitute \( x = 3 \) into \( RS = 9x \): \( RS = 9\times3 = 27 \).

Answer:

27