Question

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.Select the correct alternative.
(A) 9 cm
(B) 4 cm
(C) 6 cm
(D) 2√6 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, $\bf{option\:(C)\: correct}$

Answer 2

Solution :

Let the altitude = h cm

Let x , y are two parts of the

hypotenuse .

x = 4 cm , y = 9 cm

We know that ,

h² = xy

=> h² = 4 × 9

=> h = √36

=> h = 9 cm

Therefore ,

Option ( A ) is correct.

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