Q. 94.6( 9 Votes )

In given figure,

Answer :

Given,

∆ABC in which B = 90° and BD AC


Also, AD = 4 cm and CD = 5 cm


In ∆ADB and ∆CDB,


ADB = CDB [each equal 90°]


BAD = DBC [each equal to 90°-C]


∆DBA ∆DCB [by AAA similarity criteria]


Then,



In right angled ∆BDC,


BC2 = BD2 + CD2 [by Pythagoras theorem]


= BC2 = (2√5)2 + (5)2


= BC2 = 20 + 25 = 45


= BC = √45 = 3√5


Again,



Hence, BD = 2√5cm and AB = 6cm.


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