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

This question is inspired from Question 17 - Sample Paper for 2020 Boards - Class 10 Sample Paper

Slide62.jpeg

Slide63.jpeg
Slide64.jpeg

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

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)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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.