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Question

D and E are points on the sides AB and AC respectively of a ABC such that DE || BC

and divides ABC into two parts, equal in area. Find BDAB

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Solution

We have, Area (ADE) = Area (trapezium BCED) Area (ADE) + Area (ADE)

= Area (trapezium BCED) + Area (ADE)

2 Area (ADE) = Area (ABC)

In ADE and ABC, we have

ADE = B

[i.e, DE II BC ADE = B (Corresponding angles)]

and, A = A [Common]

ADE ~ ABC

Area of(ADE)Area of(ABC)=AD2AB2

Area of(ADE)2Areaof(ADE)=AD2AB2

12=(ADAB)2 ADAB=12

AB = 2 AD

AB = 2 (AB - BD)

( 2 - 1 ) AB = 2 BD

BDAB=212=222


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