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Question

In the given figure, if parallelogram ABCD and rectangle ABEF are of equal area then :

85009_b88ff65f581d4f49a7ce990b45cf4c6c.PNG

A
Perimeter of ABCD=Perimeter of ABEF
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B
Perimeter of ABCD < Perimeter of ABEF
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C
Perimeter of ABCD > Perimeter of ABEF
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D
Perimeter of ABCD=12 (Perimeter of ABEF)
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Solution

The correct option is B Perimeter of ABCD > Perimeter of ABEF
Given that ABEF is a rectangle and ABCD is a parallelogram, with the same base AB and have equal areas.
Since gm & rectangle have equal areas with same base AB, thereore it will be between same set of al lines.
AB=CD(1) [opposite sides of the gm]
AB=EF(2) [opposite sides of rectangle]
from (1) & (2), we get
CD=EF(3)
In ADF,
AFD=900
AD>AF [ Hypotenuse is greater than other sides.] (4)
BC>BE [Since BC=AD and BE=AF] (5)
Perimeter of gm ABCD =AB+BC+CD+DA
=AB+BC+EF+DA [from equation (3)]
>EF+FA+AB+BE [Using (5)]
which is the perimeter of rectangle ABEF.
Therefore perimeter of gm with the same base and with equal areas is greater than the perimeter of the rectangle.
Perimeter ABCD > Perimeter ABEF

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