Question : Two medians AD and BE of $\triangle$ ABC intersect at G at right angles. If AD = 9 cm and BE = 6 cm, then the length of BD (in cm) is:
Option 1: 10
Option 2: 6
Option 3: 5
Option 4: 3
Correct Answer: 5
Solution :
Given: AD = 9 cm
BE = 6 cm
$\angle$DGB = 90°
Here, the point of intersection of its medians, G divides the median in the ratio 2:1.
So, DG = $\frac{1}{3}×$AD = $\frac{1}{3}×9=3$ cm
BG = $\frac{2}{3}×$BE = $\frac{2}{3}×6=4$ cm
From Pythagoras theorem we know,
BD
2
= DG
2
+ BG
2
⇒ BD
2
= $3^2+4^2=25$
$\therefore$ BD = $\sqrt{25}=5$ cm.
Hence, the correct answer is 5 cm.
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