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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 DE divides ABC into two parts that are equal in area. Find BDAB.



A

212

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B

222

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C
(a) and (b) above.
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D
None of the above
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Solution

The correct option is C (a) and (b) above.

We have,  

Area (ADE) = Area (trapezium BCED)

Area of ABC = Area of ADE + Area of trapezium BCED

= Area of ADE + Area of ADE

= 2× Area of ADE

In ADE and ABC, we have

 ADE =  B         [Since DE || BC  ADE =  B (Corresponding angles)]

A =  A      [Common angle]

So,  ADE ~  ABC     [by AA similarity criterion]

area of  ADEarea of  ABC=AD2AB2

area of  ADE2× area of ADE=AD2AB2

Therefore  AD2AB2=12 

ADAB=12 

BDAB=ABADAB 

=1ADAB

=112

=212=222

Hence, both options (A) and (B) are correct.


Mathematics

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