Let the length of smaller square is = x in.
So the length of longer square is = (x+3)
Area of smaller square = [tex]x^2[/tex] inch^2
Area of larger square is = [tex](x+3)^2[/tex] inch^2
So sum of area of both square is 317.
[tex]x^2 + (x+3)^2 = 317[/tex]
[tex]x^2 + x^2 + 6x + 9 = 317[/tex]
[tex]2x^2 + 6x - 308 = 0[/tex]
We can write it as
[tex]x^2 + 3x - 154 = 0[/tex]
[tex]x^2 + 14x - 11x - 154 = 0[/tex]
[tex]x(x+14) - 11(x+14) = 0[/tex]
[tex](x+14)(x-11) = 0[/tex]
So x = 11 because we will neglect negative number.
So the length of smaller square is = 11 inch.
Length of larger side = 14 inch.
