Two poles A B of length a metres and C D of length a + b ( b ≠ a ) metres are erected at the same…

Two poles AB of length a metres and CD of length a+b(b≠a) metres are erected at the same horizontal level with bases at B and D. If BD=x and tan∠ACB=12, then:
  1. x2+2(a+2b)x-b(a+b)=0
  2. x2+2(a+2b)x+a(a+b)=0
  3. x2-2ax+b(a+b)=0
  4. x2-2ax+a(a+b)=0

Solution

Let ∠ABC=∠BCD=α, ∠ACB=θ 

BD=AE=x

AB=DE=a

From Diagram

tan(θ+α)=xb

tanα=xa+b

tanθ=12

tan(θ+α)=tanθ+tanα1-tanθtanα
12+xa+b1−12⋅xa+b=xb

a+b+2x2(a+b)−x=xb

ab+b2+2bx=2ax+2bx−x2

x2−2ax+ab+b2=0

x2-2ax+b(a+b)=0

Asked in: JEE Main 2021 (27 Aug Shift 2)

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