In the diagram, GB = 2x + 3..What is GB?A.5 unitsB.10 unitsC.15 unitsD.30 units
Accepted Solution
A:
Answer-[tex]\boxed{\boxed{GB=15\ units}}[/tex]Solution-From the attachment,AD = AE, so FA is a median.BD = BF, so BE is a median.CF = CE, so DC is a median.And G is the centroid.From the properties of centroid, we know thatThe centroid divides each median in a ratio of 2:1So,[tex]\Rightarrow FG:AG=2:1[/tex][tex]\Rightarrow \dfrac{FG}{AG}=\dfrac{2}{1}[/tex][tex]\Rightarrow FG=2\times AG[/tex][tex]\Rightarrow 5x=2\times (x+9)[/tex][tex]\Rightarrow 5x=2x+18[/tex][tex]\Rightarrow 3x=18[/tex][tex]\Rightarrow x=6[/tex]So, GB will be [tex]2(6)+3=15[/tex] units