Answer :

1) If then, as we know that the centroid divides each median in the ratio 2:1.


Hence,


GC/2.5 = 2/1


Cross Multiplying we get,


GC × 1 = 2 × 2.5


Therefore, I(GC) = 5


2) If then , as we know that the centroid divides each median in the ratio 2:1.


Now,


6/QG = 2/1


6 × 1 = 2 × QG


6 = 2 × QG


6/2 = QG


Hence, I(QG) = 3.


Since we have to find I(BQ), and from the figure it can be seen that,


(BQ) = I(BG) + I(QG)


Therefore, I(BQ) = 6 + 3


I(BQ) = 9.


3) If then and l(GP) = 2, as we know that the centroid divides each median in the ratio 2:1 --------(i)


Here both I(AG) and I(GP) are unknown so,


Let I(AG), I(GP) be 2x and x respectively, from equation (i)


Since, I(AP) = I(AG) + I(GP)


6 = 2x + x


6 = 3x


6/3 = x


x = 2.


Therefore, I(AG) = 2x = 2×2 = 4.


I(GP) = x = 2.


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