Question

in triangle trs, tz = (3x) inches and wz = (2x - 3) inches. what is wz?
○ 6 inches
○ 9 inches
○ 18 inches
○ 27 inches
figure may not be drawn to scale

Explanation:

Step1: Identify the centroid property

In a triangle, the centroid (point Z here) divides each median into a ratio of 2:1, so \( TZ = 2 \times WZ \).

Step2: Set up the equation

Given \( TZ = 3x \) and \( WZ = 2x - 3 \), we have \( 3x = 2(2x - 3) \).

Step3: Solve for x

Expand the right side: \( 3x = 4x - 6 \).
Subtract \( 3x \) from both sides: \( 0 = x - 6 \).
Add 6 to both sides: \( x = 6 \).

Step4: Find WZ

Substitute \( x = 6 \) into \( WZ = 2x - 3 \): \( WZ = 2(6) - 3 = 12 - 3 = 9 \).

Answer:

9 inches