Question

$\mathcal\pink{HEYA}$


PLEASE GIVE ANSWER WITH EXPLANATION ​

Answer 1

$\huge \bf \color{red}Solution:$

(1) If l(RG) = 2.5 then l(GC) = 5.

We know that the centroid divides each median in the ratio 2:1.

So, CG/RG = 2/1

CG/2.5 = 2/1

CG = 2 × 2.5

= 5

(2) If l(BG) = 6 then l(BQ) = 9.

We know that the centroid divides each median in the ratio 2:1.

So, BG/QG = 2/1

6/QG = 2/1

6 × 1 = 2 × QG

6 = 2 × QG

6/2 = QG

QG = 3.

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

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

So, I(BQ) = 6 + 3

I(BQ) = 9.

(3) If l(AP) = 6 then l(AG) = 4 and l(GP) = 2.

We know that the centroid divides each median in the ratio 2:1.

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

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

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

6 = 2x + x

6 = 3x

6/3 = x

x = 2.

I(AG) = 2x = 2×2 = 4.

I(GP) = x = 2.