in triangle trs, tz = (3x) inches and wz = (2x - 3) inches. what is wz? 6 inches 9 inches 18 inches 27…
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
Answer
Explanation:
Step1: Recall centroid property
The centroid of a triangle divides each median in a 2:1 ratio. Here, point Z is the centroid, so TZ = 2WZ.
Step2: Set up the equation
Set up the equation based on the ratio: $3x=2(2x - 3)$.
Step3: Expand the right - hand side
Expand $2(2x - 3)$ to get $3x = 4x-6$.
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: $WZ=2x - 3=2\times6-3$. $WZ=12 - 3=9$.
Answer:
9 inches