Sum of the areas of two squares is 400 cm. If the difference of their perimeters is 16 cm, find the sides of the two squares.

Explanation

Let the sides of the given square be a cm and b cm respectively , then ,
`a^(2)+b^(2) = 400`
` and 4a-4b=16implies a-b=4.`
Squaring (ii) on both sides , we get
`(a-b)^(2)=16implies(a^(2)+b^(2))-2ab = 16`
` implies 400- 2ab = 16 ["using "(i)]`
`implies 2ab=384implies ab=192.`
`Now ,(a+b)^(2)-(a-b)^(2)=4ab`
`implies (a+b)^(2)-16=4xx192.`
`implies (a+b)^(2)=768+16=784implies a+b= sqrt(784)=28.`
On solving a+b = 28 and a-b=4 , we get a= 16 and b=12.
Hence ,the sides of the given square are 16 cm and 12 cm .