Question

find the value of st if point s is between r and t, rs=16, st=2x, and rt=5x+10

Explanation:

Step1: Use segment addition postulate

Since \( S \) is between \( R \) and \( T \), we have \( RS + ST = RT \). Given \( RS = 16 \), \( ST = 2x \), and \( RT = 5x + 10 \), substitute these into the equation: \( 16 + 2x = 5x + 10 \).

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 16 = 3x + 10 \). Then subtract \( 10 \) from both sides: \( 6 = 3x \). Divide both sides by \( 3 \): \( x = 2 \).

Step3: Find \( ST \)

Substitute \( x = 2 \) into \( ST = 2x \): \( ST = 2\times2 = 4 \).

Answer:

\( 4 \)