D is the mid-point of side BC of ΔABC and E is the mid point of BD.If O is the midpoint of AE.Then Area of (ΔBOE) .
A
18Area(ΔABC)
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B
16Area(ΔABC)
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C
14Area(ΔABC)
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D
13Area(ΔABC)
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Solution
The correct option is A18Area(ΔABC)
Since AD is the median, ∴2ar(ΔABD)=ar(ΔABC) ...(i) Similarly,2ar(ΔABE)=ar(ΔABD)...(ii) And2ar(ΔBOE)=ar(ΔABE)...(iii) Now,ar(ΔABC)=2ar(ΔABD) =2[2ar(ΔABE)] from (ii) =4[2ar(ΔBOE)] from (iii) =8ar(ΔBOE) ∴18ar(ΔABC)=ar(ΔBOE)