Question

In ABC , B =90° , BD, side AC. if DC = 4cm , BD = 9cm. find AD​

Answer 1

Answer:

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

Answer 2

Answer:

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

Step-by-step explanation:

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