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Question

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.



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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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