Question

In $\Delta ABC,$ if $a=7,b=8,c=9,$ then the distance (in units) from the vertex $B$ to the centroid is

• A. $\frac{14}{3}$
• B. $\frac{7}{3}$
• C. $7$
• D. $14$

Answer 1

The correct option is A $\frac{14}{3}$


Length of median $L_{BE}:\frac{1}{2}\sqrt{2a^2+2c^2-b^2}=\frac{1}{2}\sqrt{2\times 7^2+2\times 9^2-8^2}=\frac{\sqrt{196}}{2}=7$
Using $\frac{2}{3}$ length of median through $B$
$L_{BG}=\frac{2}{3}\times L_{BE}=\frac{2}{3}\times 7=\frac{14}{3}$ units.