The difference of areas of two squares is A. The difference of their perimeters is P. The sum of their perimeters is
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,
x2 – y2=A
⇒(x−y)(x+y)=A .....(1)
Also, 4x−4y=P
⇒4(x−y)=P ⇒x−y=P4
Substituting value of x−y in (1)
(x−y)(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.