Question 30
In the given figure, ∠ACB = ∠CDA, AC = 8cm, AD = 3cm, then BD is
(a) 22/3 cm (b) 26/3 cm (c) 55/3 cm (d) 64/3 cm
Given
∠ACB = ∠CDA
In Δ ACB and Δ ADC
∠ACB = ∠ADC
∠CAB = ∠DAC
∴ Δ ACB ∼ Δ ADC
We know that
Sides of similar triangle are in same proportion
∴ 𝐴𝐶/𝐴𝐷 = 𝐴𝐵/𝐴𝐶
Putting values
8/3 = 𝐴𝐵/8
8/3 = 𝐴𝐵/8
8/3 × 8 = AB
64/3 = AB
AB = 𝟔𝟒/𝟑
Now,
BD = AB − AD
= 64/3 − 3
= (64 − 9)/3
= 𝟓𝟓/𝟑 cm
So, the correct answer is (c)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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