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Question

Let ABCD is a square with sides of unit length. Point E and F are taken on sides AB and AD respectively so that AE=AF. Let P be a point inside the square ABCD.

The maximum possible area of quadrilateral CDFE is?

A
18
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B
14
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C
58
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D
38
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Solution

The correct option is C 58

We have, the sides of square ABCD is unit.
AB=BC=CD=DA=1unit
Now, according to the question,
ar(EAF)=12×x×x

ar(EAF)=12x2

ar(EBC)=12×(1x)×1

ar(EBC)=12(1x)

ar(ABCD)=1×1=1
Now,
ar(CDFE)=ar(ABCD)ar(EAF)ar(EBC)

=1x22(1x)2

=2x2(1x)2

=1+xx22

Area of quadrilateral CDFE =1+xx22

=1+12(12)22 [ Since, x=12 ]

=32142

=58



1462679_1350549_ans_0f7a5b1a6ea741e08083e680dd935513.png

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