In ΔABC angle ∠C = 90° and M and n are mid points of the sides AB and AC respectively. CM and BN intersect each other at D and ∠BDC = 90°. If BC = 12 cm, then the length of BN is ?
Answer & explanation
Correct answer: option 1
BN and CM are the medians
So, D divide BN in the ratio 2 : 1
⇒ BD : DN = 2 : 1
Let BD = 2x , DN = x
⇒ BN = 3x
In ΔCNB, CD is perpendicular to BN
(BC)2 = (BD) × (BN)
(12)2 = 2x × 3x
144 = 6x2 ⇒ x2 = \(\frac{144}{6}\)
x = 2\(\sqrt {6}\) cm
3x = 3(2\(\sqrt {6}\) )cm = 6\(\sqrt {6}\) cm