Question

The sum of the areas of two squares is 640cm^2.if the difference between their perimeters is 64cm,then find sides of the squares

Answer 1

Side of first square is 32 cm and of other is 8 cm

1) Let the side of square 1 be x and side of second square be y.

2) $x^{2} +y^{2} = 640$ and 4x-4y = 64 cm, so x-y =16

3) Squaring the second equation (x-y)^2 = 16^2.

4) x^2+y^2 -2xy = 256

5) Substituting, xy = 192

6) Now, find the (x+y)^2 and then x+y

7) (x+y)^2 = x^2+ y^2+ 2xy = 1024 and x+y = 32

8) x+y = 32 and x-y = 16

9) This gives x = 24 and y = 8