Question

2. Altitude on the hypotenuse of a right angled triangle divides it in
two parts of lengths 4 cm and 9 cm. Find the length of the altitude
(A) 9 cm (B) 4 cm (C) 6 cm (D) 26 cm​

Answer 1

ABC right angle triangle is drawn in such a way that ∠ABC = 90° . D is the point on side AC where BD ⊥ AC . Also D divides the side length AC in two parts AD and DC of lengths 9cm and 4 cm respectively.

Now, from ∆ABD and ∆BDC

∠ADB = ∠BDC = 90°

∠BAD = ∠DBC [ see figure , if we assume ∠DBC = x° then, DBA = 90 - x° then from ∆ABD , ∠BAD = x° ]

from A - A similarity rule ,

∆DAB ~ ∆DBC

so, BD/DC = AD/BD

⇒BD² = DC × AD = 4cm × 9 cm

taking square root both sides,

BD = 6 cm

Hence , altitude = 6cm

So, $Option$ $(C)$ $is$ $correct$