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Question
In figure, MN || BC and AM : MB = 1 : 2, then `(ar(ΔAMN))/(ar(ΔABC))` = ______.
Fill in the Blanks
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Solution
In figure, MN || BC and AM : MB = 1 : 2, then `(ar(ΔAMN))/(ar(ΔABC))` = `underline(1/9)`.
Explanation:
Here, AM = k, MB = 2k.
And MN || BC
∴ AB = AM + MB
= k + 2k
= 3k
∴ `(ar(ΔAMN))/(ar(ΔABC)) = (AM^2)/(AB^2)`
= `k^2/(9k^2)`
= `1/9`
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