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Question

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

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 ABEFGiven 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 getCD=EF⟶(3)In △ADF,∠AFD=900AD>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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