Question

In the given figure, ∠ ABC = 900 and BD 丄 AC. if AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm. Find BC.

Answer 1

Answer: BC = 8.1

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

∠BCD=∠ABD

∠DBC=∠DAB

So by AAA

△BDC∼△ADB

Hence

CD

BC

=

BD

AB

5.4

BC

=

3.8

5.7

BC=8.1

Hence BC=8.1cm