AD is the median of ΔABC. G is the centroid of ΔABC. If AG = 14 cm, then what is the length of AD ?

21 cm

Concept Used

Centroid = intersection of the medians

Centroid divides median in ratio of 2 : 1

Calculation

We know that G is centroid of \(\Delta \)ABC

AG = 14 cm

Also, AG : GD = 2 : 1

= \(\frac{AG}{GD}\) = \(\frac{2}{1}\)

= GD = \(\frac{AG}{2}\)

= GD = \(\frac{14}{2}\) =  7 cm

= AD = AG + GD

= 14 + 7 = 21 cm.

Therefore, AD is 21 cm.