Question

in triangle trs, tz = (3x) inches and wz = (2x - 3) inches. what is wz? 6 inches 9 inches 18 inches 27 inches

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median in a 2:1 ratio. Here, point Z is the centroid of triangle TRS, so TZ = 2WZ.

Step2: Set up equation

Set up the equation based on the ratio: $3x=2(2x - 3)$.

Step3: Expand right - hand side

Expand $2(2x - 3)$ to get $4x-6$. So the equation becomes $3x=4x - 6$.

Step4: Solve for x

Subtract $3x$ from both sides: $0=x - 6$. Then add 6 to both sides to find $x = 6$.

Step5: Find WZ

Substitute $x = 6$ into the expression for WZ: $WZ=2x-3=2\times6 - 3=12 - 3=9$.

Answer:

9 inches