in triangle abc, eg = x inches and bg = (5x - 12) inches. what is eb? 2 inches 4 inches 8 inches 12 inches…
in triangle abc, eg = x inches and bg = (5x - 12) inches. what is eb? 2 inches 4 inches 8 inches 12 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, G is the centroid and BG = 2EG.
Step2: Set up the equation
Since BG = 2EG, we have the equation $5x - 12=2x$.
Step3: Solve for x
Subtract 2x from both sides: $5x-2x - 12=2x-2x$, which simplifies to $3x-12 = 0$. Then add 12 to both sides: $3x=12$, and divide by 3 to get $x = 4$.
Step4: Find EB
EB=BG - EG. Since EG=x = 4 and BG = 5x - 12=5×4 - 12=8, then EB=8 - 4=4.
Answer:
4 inches