In ΔABC, AC = BC, and the length of the base AB is 10 cm. If CG = 8 cm, where G is the centroid, then what is the length of AC ?

13 cm

We know that,

The medians are divided into a 2 :1 ratio by the centroid

We have,

AC = BC,

AB = 10 cm.

CG = 8 cm

In the diagram, CD is median,

So, GD = 4 cm

AD = BD = 5 cm

As ΔABC is an Isosceles triangle ,

So, AC = √(12² + 5²)

= AC = √(144 + 25)

= AC = √169 = 13