Question

In the given figure ∠ABC=90°


, BD ⊥ AC. If AB=6cm, BC=8cm, CA=10cm then

the length of AD is a)6.3cm b)3.6cm c)3cm d)4cm​

Answer 1

Step-by-step explanation:

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:

5cm

Step-by-step explanation:

because cd is longer then ab