In triangle XYZ, G is the centroid, If XY = 11 cm, YZ = 14 cm and XZ = 7 cm, then what is the value (in cm) of GM?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 2
G is the centroid here
By Apollonius theorem,
112 + 72 = (72 + MX2) × 2
⇒ MX2 = 1/2 × (112 - 72)
⇒ MX2 = 1/2 × 18 × 4
⇒ MX2 = 36
⇒ MX = 6
Hence,
GM = 1/3 × 6 = 2 cm