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SSC CHSL 2020 · Question 47 of 91

In a triangle ABC, ∠BAC = 90° and AD is perpendicular to BC. If AD = 8.4 cm and BD = 4.8 cm, then the length of BC is

Geometry

  1. A18.5 cm
  2. B15 cm
  3. C18 cm
  4. D19.5 cmCorrect

Answer: D. 19.5 cm

Explanation

Given: Calculation: In ΔADB, Using pythagoras theorem, ⇒ AB 2= BD 2+ AD 2 In ΔADC, Using pythagoras theorem, ⇒ AC 2= AD 2+ DC 2 In ΔBAC, Using pythagoras theorem, ⇒ BC 2= AB 2+ AC 2 ⇒ (4.8 + DC) 2= 4.8 2+ 8.4 2+ (8.4 2+ DC 2) ⇒ 4.8 2+ 9.6DC + DC 2= 4.8 2+ 8.4 2+ (8.4 2+ DC 2) ⇒ 9.6DC = 2 × 8.4 × 8.4 ⇒ DC = (8.4 × 2.1)/1.2 = 14.7 cm ∴ BC = BD + DC = 4.8 + 14.7 = 19.5 cm

Source: SSC CHSL 2020 (Tier-I) Prev. Year Paper (04-Aug-2021) (Shift 1) — prepp.in solved paper · reliable-secondary

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