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 15 cm $\sqrt{91}$ cm 12 cm

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