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Question
In the given figure, AE = 5 cm and EC = 7 cm, then area of ΔADE: area of ΔABC is ______.
Options
5 : 7
7 : 5
25 : 144
144 : 25
MCQ
Fill in the Blanks
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Solution
In the given figure, AE = 5 cm and EC = 7 cm, then area of ΔADE: area of ΔABC is 25 : 144.
Explanation:
From figure,
In △ ADE and △ ABC,
⇒ ∠DAE = ∠BAC (Common angle)
⇒ ∠ADE = ∠ABC (Corresponding angles are equal)
∴ △ ADE ~ △ ABC (By A.A. postulate)
From figure,
AC = AE + EC = 5 + 7 = 12 cm.
We know that,
The areas of two similar triangles are proportional to the squares on their corresponding sides.
∴ `("Area of" △ ADE)/("Area of "△ ABC) = (AE^2)/(AC^2)`
= `5^2/12^2`
= `25/144`
= 25 : 144
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