Question

Seg AD and seg BE are medians of ∆ ABC and point G is the centroid. If l (AG) = 5 cm, find l (GD). IF l (GE) = 2 cm, find l (BE).

Answer 1

Given: In ∆ABC, AD and BE are medians and point G is the centroid such that AG = 5 cm, and GE = 2 cm.



GD = ? and BE = ?

In ∆ABC,

Since, G is the centroid and AD is median.

So,

$$\begin{gathered} \mathrm{AG}:\mathrm{GD}=2:1 \\ \Rightarrow \frac{\mathrm{AG}}{\mathrm{GD}}=\frac{2}{1} \\ \Rightarrow \frac{5}{\mathrm{GD}}=2 \\ \Rightarrow \mathrm{GD}=\frac{5}{2} \\ \therefore \mathrm{GD}=2.5\mathrm{cm} \end{gathered}$$

Similarly,

Since, G is the centroid and BE is median.

So,

$$\begin{gathered} \mathrm{BG}:\mathrm{GE}=2:1 \\ \Rightarrow \frac{\mathrm{BG}}{\mathrm{GE}}=\frac{2}{1} \\ \Rightarrow \frac{\mathrm{BG}}{2}=2 \\ \Rightarrow \mathrm{BG}=2\times 2 \\ \Rightarrow \mathrm{BG}=4\mathrm{cm} \\ \therefore \mathrm{BE}=\mathrm{BG}+\mathrm{GE}=4+2=6\mathrm{cm} \end{gathered}$$