Question

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​In a triangle ABC, E is the mid-point of median AD. Show that ar(BED) = ¼ ar(ABC).
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Answer 1

Solution :

Given:

In AABC, AD is the median and E is the mid point of AD

A median divides the a triangle into two triangles with equal area

Area AABD = Area AADC

Now

+ (1)

Area AABC = Area AABD + Area AADC

Area AABC = 2(Area AABD)

[: From (1)]

> Area AABD = 1 X Area AABC (2)

BE is the median of AABD So.

Area AABE Area ABED +(3)

Area AND = Area AABE + Area ABED

Area AABD = 2(Area ABED)

1 2 x Area AABC = 2(Area ABED)

1 4 x Area AABC = Area ABED

. Area ABED = 1 4 X Area ΔABC

Hence proved

Answer 2

Answer:

Given ABC is a triangle in which E is the mid-point of the median.

Since median of a triangle divides a triangle into two equal triangles of equal area.

So area of Δ ABD = 1/2 * area of Δ ABC

Again BE is the median of the triangle ABD

So area of Δ BDE =1/2* area of Δ ABD

= 1/2*1/2* area

of Δ ABC

= 1/4 * area of Δ ABC

So area of Δ BDE = 1/4 * area of Δ ABC

Step-by-step explanation:

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