G is the centroid of a triangle ABC, whose sides AB = 35 cm, BC = 12 cm, and AC = 37 cm. The length of BG is (correct to one decimal place):

Answer: Option D

AB = 35 cm, BC = 12 cm and AC = 37 cm
12, 35 and 37 are triplet

ABC is a right angle triangle at ∠B = 90°
Use appoloneous theorem
$$\begin{array}{rl}& A{B}^2+B{C}^2=2\left(A{D}^2+B{D}^2\right)\\ & 35^2+12^2=2\times {\left(\frac{AC}{2}\right)}^2+2B{D}^2\\ & 37^2=2\times {\left(\frac{37}{2}\right)}^2+2B{D}^2\\ & 2B{D}^2=37^2\left(1-\frac{1}{2}\right)\\ & 2B{D}^2=1369\times \frac{1}{2}\\ & B{D}^2=\frac{1369}{4}\\ & BD=\frac{37}{2}\\ & BG=BD\times \frac{2}{3}\\ & BG=\frac{37}{2}\times \frac{2}{3}\\ & BG=\frac{37}{3}=12.3\text{ cm}\end{array}$$