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)
Made by
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.
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