Question

In the given figure Angle 90° AD perpendicular BD=2cm and CD=8cm Find AD​

Answer 1

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