Pls answer Q.51
Need Qualitative Answers with good explanation.
Answers
To prove Δ AEF and Δ ABC similar :
∠EAF = ∠BAC [ Common ]
∠AEF = ∠ABC [ corresponding ∠s ]
Δ AEF ≈ Δ ABC [ A.A criteria ]
So : AE : AB = EF : BC [ corresponding ∠s of Δ ]
Finding EF
So : AE / AB = EF / BC
==> AE / AB = EF / 15 cm
==> AB / AE = 15 cm / EF [ Invertendo ]
==> AB / AE - 1 = 15 / EF - 1
==> ( AB - AE ) / AE = ( 15 - EF ) / EF
==> EB / AE = ( 15 - EF ) / EF
==> 3 / 2 = ( 15 - EF ) / EF
==> 3 EF = 30 - 2 EF
==> 5 EF = 30
==> EF = 30 / 5
==> EF = 6
EF = 6 cm ....................(1)
Similarly : Δ CFG ≈ Δ ACD
Finding FG
FG : AD = CG : CD
Given : AE : EB = 2 : 3
So : DG : CF = 2 : 3 ..............................(2)
==> We know that : -
AD / FG = DC / CG [ corresponding parts of similar Δ ]
==> AD / FG - 1 = DC / CG - 1
==> ( AD - FG ) / FG = ( DC - CG ) / CG
AD = BC = 15 cm
==> ( 15 - FG ) / FG = DG / CG
==> ( 15 - FG ) / FG = 2 / 3 [ See (2) ]
==> 45 - 3 FG = 2 FG
==> 5 FG = 45
==> FG = 45/5
==> FG = 9
FG = 9 cm
Difference between EF and FG
FG = 9 cm
( - ) EF = 6 cm
-----------------------
FG - EF = 3 cm
Hope it helps !
______________________________________________________________________
Answer:
Step-by-step explanation:To prove Δ AEF and Δ ABC similar :
∠EAF = ∠BAC [ Common ]
∠AEF = ∠ABC [ corresponding ∠s ]
Δ AEF ≈ Δ ABC [ A.A criteria ]
So : AE : AB = EF : BC [ corresponding ∠s of Δ ]
Finding EF
So : AE / AB = EF / BC
==> AE / AB = EF / 15 cm
==> AB / AE = 15 cm / EF [ Invertendo ]
==> AB / AE - 1 = 15 / EF - 1
==> ( AB - AE ) / AE = ( 15 - EF ) / EF
==> EB / AE = ( 15 - EF ) / EF
==> 3 / 2 = ( 15 - EF ) / EF
==> 3 EF = 30 - 2 EF
==> 5 EF = 30
==> EF = 30 / 5
==> EF = 6
EF = 6 cm ....................(1)
Similarly : Δ CFG ≈ Δ ACD
Finding FG
FG : AD = CG : CD
Given : AE : EB = 2 : 3
So : DG : CF = 2 : 3 ..............................(2)
==> We know that : -
AD / FG = DC / CG [ corresponding parts of similar Δ ]
==> AD / FG - 1 = DC / CG - 1
==> ( AD - FG ) / FG = ( DC - CG ) / CG
AD = BC = 15 cm
==> ( 15 - FG ) / FG = DG / CG
==> ( 15 - FG ) / FG = 2 / 3 [ See (2) ]
==> 45 - 3 FG = 2 FG
==> 5 FG = 45
==> FG = 45/5
==> FG = 9
FG = 9 cm
Difference between EF and FG
FG = 9 cm
( - ) EF = 6 cm
-----------------------
FG - EF = 3 cm
Hope it helps !
______________________________________________________________________
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