Question

In the given figure angle ABC = 90 degree and BD is perpendicular to AC if BD = 8cm and AD = 4cm . then find the value of CD.​

Answer 1

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

Answer 2

Answer:

Given ∠ABC=90°,BD is perpendicular to AC, BD=8,and, AD=4, as shown in the diagram.

Let ∠ACB=x,⇒∠CBD=90−x

⇒∠ABD=x,⇒∠BAD=90−x

⇒ΔABC,ΔADB,andΔBDC are similar

⇒BD/CD=AD/DB

⇒8/CD=4/8

⇒CD=8×8/4=16

hope it helps