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Question 9
In given figure, ABC is a triangle right angled at B and BDAC. If AD =4 cm and CD = 5cm, then find BD and AB.



 


Solution

Given, ΔABC in which B=90 and BDAC.

Also,    AD = 4cm and CD = 5cm          
In ΔADB and ΔCDB,
 ADB=CDB  [each equal to 90]
 BAD=DBC [each equal to 90C ]
   ΔDBAΔDCB     [by AAA similarity criterion]
Then, DBDA=DCDB
 DB2=DA×DC
 DB2=4×5
 DB=25cm

In right angled ΔBDC,  
 BC2=BD2+CD2  [ by Pyathogoras theorem] 
 BC2=(25)2+(5)2
=20+25=45
 BC=45=35
Again, ΔDBAΔDCB,
   DBDC=BABC
 255=BA35
   BA=25×355=6cm
Hence, BD=25cm and AB=6 cm

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