In `triangleABC`, it is given that D is the midpoint of BC, E is the m – InterviewSolution

InterviewSolution

1.	In `triangleABC`, it is given that D is the midpoint of BC, E is the midpoint of BD and O is the midpoint of AE. Then, `ar(triangleBOE)` = ? A. `(1)/(3)ar(triangleABC)`B. `(1)/(4)ar(triangleABC)`C. `(1)/(6)ar(triangleABC)`D. `(1)/(8)ar(triangleABC)`
Answer» Correct Answer - D Median AD divides `triangleABC` into two `triangle` of equal area. `therefore ar(triangleABD)=(1)/(2)ar(triangleABC)`. Median AE divides `triangleABD` into two `triangle` of equal area. `therefore ar(triangleABE)=(1)/(2)ar(triangleABD)=(1)/(4)ar(triangleABC)`. Median OB divides `triangleABE` into two `triangle` of equal area. `therefore ar(triangleBOE)=(1)/(2)ar(triangleABE)=(1)/(8)ar(triangleABC)`.

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