Question

Que: In a triangle ABC, E is the mid-point of median AD. Show that ar(BED) = 1/4 ar(ABC).

Answer 1

Answer:

Solution:

ar(BED) = ½ × BD × DE

Since, E is the mid-point of AD,

AE = DE

Since, AD is the median on side BC of triangle ABC,

BD = DC

DE = ½ AD — (i)

BD = ½ BC — (ii)

From (i) and (ii), we get,

ar(BED) = (1/2) × (½) BC × (1/2)AD

⇒ ar(BED) = (½) × (½) ar(ABC)

⇒ ar(BED) = ¼ ar(ABC)

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Answer 2

Answer:

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