In the given figure Angle 90° AD perpendicular BD=2cm and CD=8cm Find AD
Question
In the given figure Angle 90° AD perpendicular BD=2cm and CD=8cm Find AD
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Mathematics
2 years
2021-07-08T05:30:44+00:00
2021-07-08T05:30:44+00:00 1 Answers
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Answers ( )
Given:
∠BDC=90
∘
∠ABC=90
∘
Let ∠BCD=x
∘
Using triangle sum property in △BDC, ∠DBC=90−x
∘
Also ∠ABD=x
∘
Using triangle sum property in △ADB, ∠BAD=90−x
∘
Now considering △BDC and △ADB
∠BDC=∠BDA [∵∠BDC=∠BDA=90
∘
]
∠DBC=∠DAB [∵∠DBC=∠DAB=(90−x)
∘
]
So by AA
△BDC∼△ADB
Hence
CD
BD
=
BD
AD
CD
8
=
8
4
CD=16
Hence CD=16cm