Question

find the measure of sw. enter your answer as a number.
answer

Explanation:

Step1: Identify RT as perpendicular bisector

Since \( RT \perp WS \) and \( RW = RS \) (marked congruent), \( RT \) bisects \( WS \). So \( WT = TS \).

Step2: Set up equation for \( WT \) and \( TS \)

\( 4x - 4 = 2x + 2 \)

Step3: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 2x - 4 = 2 \)
Add 4 to both sides: \( 2x = 6 \)
Divide by 2: \( x = 3 \)

Step4: Find \( SW \)

\( SW = WT + TS = (4x - 4) + (2x + 2) \). Substitute \( x = 3 \):
\( WT = 4(3) - 4 = 8 \), \( TS = 2(3) + 2 = 8 \)
\( SW = 8 + 8 = 16 \)

Answer:

16