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Question
In ΔABC, and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.
Solution
Since, D and E are the mid-points of AB and AC respectively.
Therefore, DE || BC.
Consequently,
ΔADE ∼ ΔABC
⇒ `"area (ΔADE)"/"area (ΔABC)" = "AD"^2/"AB"^2`
= `"AD"^2/(2"AD")^2`
= `(1)/(4)` ...{∵ AB = 2AD)
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