Question

Altitude on the hypotenuse of a right angled triangle divides it in two parts of lengths 4cm and 9cm. find the length of the altitude.​

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.(see attachment for help)

                                    or

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.

••••