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Question

A rectangle and a parallelogram of equal area and equal base are given. If r and p denote their respective perimeters, then

A
r=p
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B
r=2p
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C
r>2p
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D
r<p
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Solution

The correct option is D r<p
Perimeter of the rectangle ABCD
=(AB+AD)+(DC+BC)=r ........(i)

Perimeter of parallelogram ABFE
=(AB+AE)+(EF+BF)=p ........(ii)

in right angled ADE
AE>AD ...[since being the hypotenuse side]

in right angled BCF
=>BF>BC ...[since being the hypotenuse side]

Also, AB=DC and AB=EF ( opposite sides of a rectangle and a parllelogram are equal )
=>DC=EF

Comparing (i) & (ii), we get
Perimeter of rectangle<Perimeter of Parallelogram (both BF and AE are greater than BC and AD respectively)

i.e. r<p

311793_284321_ans_7dafd903eef44a18983f5f933801cf3e.png

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