Answer :

Area of a square = s2


Perimeter of a square = 4s


Let the sides of the square be a and b respectively.


Given, sum of the areas of two squares is 400 cm2 and the difference of their perimeters is 16 cm.


a2 + b2 = 400 and


4a – 4b = 16


a – b = 4


a = 4 + b


(4 + b)2 + b2 = 400


2b2 + 8b + 16 = 400


b2 + 4b – 192 = 0


b2 + 16b – 12b – 192 = 0


(b + 16)(b – 12 ) = 0


b = 12 m


Thus, a = 16 m


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