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प्रश्न
In the given figure, AD : DB = 2 : 5, then area of ∆ODE : area of ∆OCB is ______.
पर्याय
4 : 49
49 : 4
4 : 25
25 : 4
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उत्तर
In the given figure, AD : DB = 2 : 5, then area of ∆ODE : area of ∆OCB is 4 : 49.
Explanation:
Given,
AD : DB = 2 : 5
Let AD = 2x and DB = 5x
From figure,
AB = AD + DB = 2x + 5x = 7x
In △ ADE and △ ABC,
⇒ ∠DAE = ∠BAC (Common angle)
⇒ ∠ADE = ∠ABC (Corresponding angles are equal)
∴ △ ADE ~ △ ABC (By A.A. postulate)
We know that,
Corresponding sides of similar triangles are in proportion.
∴ `(DE)/(BC) = (AD)/(AB)`
⇒ `(DE)/(BC) = (2x)/(7x)`
⇒ `(DE)/(BC) = 2/7`
In △ ODE and △ OCB,
⇒ ∠DOE = ∠BOC (Vertically opposite angle are equal)
⇒ ∠ODE = ∠OCB (Alternate angles are equal)
∴ △ ODE ~ △ OCB (By A.A. postulate)
We know that,
The areas of two similar triangles are proportional to the squares on their corresponding sides.
⇒ `("Area of" △ ODE)/("Area of" △ OCB) = (DE^2)/(BC^2)`
= `2^2/7^2`
= `4/94`
= 4 : 49
