In ∆ABC, ˂B = 90° and BD ꓕ AC. If AC = 9cm and AD = 3 cm then BD is equal to

(a) 2√2cm   (b) 3√2  cm   (c) 2√3  cm   (d) 3 √3 cm

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  1. Class 10
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Question 23 In ∆ABC, ˂B = 90° and BD ꓕ AC. If AC = 9cm and AD = 3 cm then BD is equal to (a) 2√2cm (b) 3√2 cm (c) 2√3 cm (d) 3 √3 cm Let ∠ A = x° In Δ ABC ∠ ACB = 90° − x And, in Δ ABD ∠ ABD = 90° − x For Δ ABD and Δ BCD ∠ ABD = ∠ BCD ∠ BAC = ∠ DAB ∴ Δ ABD ~ Δ BCD Since sides in similar triangle are proportional 𝑨𝑫/𝑩𝑫=𝑩𝑫/𝑪𝑫 3/𝐵𝐷=𝐵𝐷/6 3 × 6 = BD2 18 = BD2 BD2 = 18 BD2 = 9 × 2 BD2 = 32 × 2 BD = 3 × √2 BD = 3 √𝟐 cm So, the correct answer is (b)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.