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Question

The difference of areas of two squares is A. The difference of their perimeters is P. The sum of their perimeters is


A

2AP

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B

16AP

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C

4AP

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D

8AP

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Solution

The correct option is B

16AP


Let the sides of squares be x and y

Then their areas are x2,y2

Their perimeters are 4x,4y

Sum of their perimeters = 4x+4y = 4(x+y)

Given,
x2y2=A

(xy)(x+y)=A .....(1)

Also, 4x4y=P

4(xy)=P xy=P4

Substituting value of xy in (1)

(xy)(x+y)=A

P4(x+y)=A

(x+y)=4AP

4(x+y)=16AP [Multiplying both sides by 4, as we need sum of perimeters]

Therefore, the sum of their perimeters is 16AP.


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