Question

In ΔABC, and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.

Answer 1

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)