Question

In the given figure, If DE || BC and AD : DB = 1:2 then Area of ∆ADE/Area of ∆ABC
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Answer 1

Answer:

1:9

Step-by-step explanation:

AB = AD + BD = 1 + 2 = 3

Ar(ADE) : Ar(ABC) = (1/3)^2 = 1:9

Answer 2

Given : DE || BC and AD : DB = 1:2

To find : Area of ∆ADE/Area of ∆ABC

Solution:

DE || BC

=> ΔADE  ≈ ΔABC

(Area of ΔADE)/ (Area of ΔABC)  =   (AD / AB) ²

AD : DB  = 1:2

=> AD/DB  = 1/2

=> DB = 2AD

AB = AD  + DB

=> AB = AD + 2AD

=> AB = 3AD

(Area of ΔADE)/ (Area of ΔABC)  =   (AD / 3AD) ²

(Area of ΔADE)/ (Area of ΔABC)  =   (1/ 3 ) ²

(Area of ΔADE)/ (Area of ΔABC)  =    1/ 9

Area of ∆ADE/Area of ∆ABC = 1/9

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