Please solve q 105 ?

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1 Answer
CW
May 26, 2018

(2) " " sqrt6-sqrt3(2) √6−√3

Explanation:

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Let |ABC||ABC| denote area of ABCABC
Given AD=3, => |ABC|=1/2*3*BC=3/2BCAD=3,⇒|ABC|=12⋅3⋅BC=32BC
let |ABC|=3a, => a=1/2BC|ABC|=3a,⇒a=12BC,
=> |AGH|=a=1/2BC⇒|AGH|=a=12BC
=> |AJK|=2a=BC⇒|AJK|=2a=BC
As DeltaABC, DeltaAJK and DeltaAGH are similar,
=> JK^2:BC^2=2a:3a=2:3
=> JK:BC=sqrt2:sqrt3, => color(red)(JK=sqrt2/sqrt3*BC)
Similarly, GH^2:BC^2=1a:3a=1:3
=> GH:BC=1:sqrt3, => color(red)(GH=1/sqrt3* BC)
Now, |AJK|=2a=BC=1/2*AF*JK,
=> AF=(2BC)/(JK)=2BC*sqrt3/(sqrt2BC)=sqrt6
Similarly, |AGH|=a=1/2BC=1/2*AE*GH
=> AE=(BC)/(GH)=BC*sqrt3/(BC)=sqrt3
=> EF=AF-AE=sqrt6-sqrt3 units

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