Question

18. AABC is a right angled triangle where ZB = 90° and BDI AC. (
If BD = 8 cm, AD = 4 cm, then CD is
(A) 24 cm
(B) 16 cm
(C) 32 cm
(D) 8 cm​

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