Question

In triangle ABC, AB=9,BC=10,AC=13 if G is centroid and D is mid point of BC then the length of GD

Answer 1

AD is a median of ABC. We have (standard formula):

AD² = ¼(2AB² + 2AC² - BC²)

= ¼(2 x 9² + 2 x 13² - 10²)

= ¼(162 + 338 - 100)

= ¼ x 400 =100

AD = 10

GD = ⅓AD = 10/3.