Question

use the figure on the right to find tw.

tw = (type an integer or a decimal.)

Explanation:

Step1: Use the perpendicular bisector theorem

Since \( TY = YZ \) and \( WY\perp TZ \), by the perpendicular bisector theorem, \( TW = WZ \).

Step2: Set up the equation

We know \( TW = 2x \) and \( WZ = 5x - 6 \). So, \( 2x=5x - 6 \).

Step3: Solve the equation for \( x \)

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

Step4: Find \( TW \)

Substitute \( x = 2 \) into \( TW = 2x \). So, \( TW=2\times2=4 \).

Answer:

\(4\)