In a triangle ABC, G is the centroid. If AB = 11 cm, BC = 14 cm and AC = 7 cm then find the value of GX(in cm)?
Answer & explanation
Correct answer: option 4
Length of median (AX) = \(\frac{1}{2}\)\(\sqrt {2(AB)^2 + 2(AC)^2 - (BC)^2}\)
= \(\frac{1}{2}\)\(\sqrt {2(AB)^2 + 2(AC)^2 - (BC)^2}\)
= \(\frac{1}{2}\)\(\sqrt {(144)}\) = \(\frac{1}{2}\) × 12 = 6 cm
⇒ Centroid divide median in ratio
⇒ GX = \(\frac{1}{3}\)(AX) = \(\frac{1}{3}\) × 6 = 2 cm