A
4 cm
D
8 cm
с
B
Fig. 7.137
C
Answers
Answered by
0
Answer:
A
4 cm
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Answered by
2
Step-by-step explanation:
In the given figure,∠ ABC = 90 and B D ⊥ AC. If BD = 8 cm and AD = 4 cm, find CD.
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
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