Question

v is a point on segment (overline{uw}). if (uv = 13), (vw = x + 15), and (uw = 2x + 12), what is (vw)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

Since \( V \) is on \( \overline{UW} \), we have \( UV + VW = UW \). Substituting the given values: \( 13 + (x + 15) = 2x + 12 \).

Step2: Simplify and solve for \( x \)

Simplify left side: \( 13 + x + 15 = x + 28 \). So equation is \( x + 28 = 2x + 12 \). Subtract \( x \) from both sides: \( 28 = x + 12 \). Subtract 12: \( x = 16 \).

Step3: Find \( VW \)

Substitute \( x = 16 \) into \( VW = x + 15 \): \( VW = 16 + 15 = 31 \).

Answer:

31