Question

Q.8 In triangle ABC,angle ABC=90
degree and BD perpendicular to CD,
if BD = 8 cm. AD = 4 cm then x = CD
will be---​

Answer 1

Given

∠

A

B

C

=

90

∘

,

B

D

is perpendicular to

A

C

,

B

D

=

8

,

and

A

D

=

4

, as shown in the diagram.

Let

∠

A

C

B

=

x

,

⇒

∠

C

B

D

=

90

−

x

⇒

∠

A

B

D

=

x

,

⇒

∠

B

A

D

=

90

−

x

⇒

Δ

A

B

C

,

Δ

A

D

B

,

and

Δ

B

D

C

are similar

⇒

B

D

C

D

=

A

D

D

B

⇒

8

C

D

=

4

8

⇒

C

D

=

8

×

8

4

=

16

Answer 2

➛ Sσlutíσn :

Let ∠ACB = x, ∠ABD = x, ∠CBD = 90-x° and

∠BAD = 90-x°

ΔABC , ΔABD and ΔBDC are similar,

$\implies$ $\displaystyle{\sf{ \frac{BD}{CD} = \frac{AD}{DB}}}$

$\implies$$\displaystyle{\sf{ \frac{4}{CD} = \frac{4}{8}}}$

$\implies$ $\displaystyle{\sf{ CD = \frac{8 \times 8 }{4} = 16}}$