30. In the given figure, /_ ACB = /_ CDA, AC = 8cm, AD = 3cm, then BD is
(A) 22/3 cm (C) 55/3 cm (B) 26/3 cm (D) 64/3 cm
Answers
Answer:
Option (C)
BD = 55/3 cm
Step-by-step explanation:
Given :-
∠ACB = ∠ACD
AC = 8 cm
AD = 3 cm
To find :-
The length of BD
Solution :-
Given that
< ACB = < ACD
AC = 8 cm
AD = 3 cm
From the given figure ,
∆ ACB and ∆ ADC
∠ACB = ∠ACD (Given )
∠CAB = ∠DAC ( Common angle )
By A.A. Criteria for similarity
∆ ACB and ∆ ACD are similar triangles
Therefore, ∆ ACB ~ ∆ ACD
We know that
In two similar triangles , Corresponding sides are in the same ratio or in proportion.
Therefore, AC / AD = AB / AC
On applying cross multiplication then
=> AC × AC = AD × AB
=> 8 × 8 = 3 × AB
=> 64 = 3 AB
=> 3 AB = 64
=> AB = 64/3 cm
Therefore, AB = 64/3 cm
From the given figure ,
AB = AD + DB
=> 64/3 = 3 + BD
=> (64/3) - 3 = BD
=> BD = (64-9)/3
=> BD = 55/3 cm
Therefore, BD = 55/3 cm
Answer :-
The length of BD is 55/3 cm
Used formulae:-
A A criteria for similarity :-
"In two triangles , two angles in one triangle respectively equal to the corresponding two angles in the other triangle then they are similar triangles and this is A.A. criteria for similarity.
→ The ratio of the corresponding sides are in the same ratio or in proportion in similar triangles .
Refer the given attachment
