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. .......... Please answer fast friends. ....Please no spam answer a. ........

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