Question

in triangle abc, eg = x inches and bg = (5x - 12) inches. what is eb? 2 inches 4 inches 8 inches 12 inches

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 and EG = x, BG = 5x - 12, we have 5x - 12=2x.

Step3: Solve for x

Subtract 2x from both sides: 5x-2x - 12=2x - 2x, which gives 3x - 12 = 0. Then add 12 to both sides: 3x-12 + 12=0 + 12, so 3x = 12. Divide both sides by 3: $\frac{3x}{3}=\frac{12}{3}$, and x = 4.

Step4: Find EB

EB=BG - EG. Since EG = x = 4 and BG = 2x = 8, then EB=8 - 4 = 4 inches.

Answer:

4 inches