Drawing a diagonal line through a square or rectangle makes 2 right triangles. The line drawn will be the hypotenuse of the triangles, which is the longest side.
By using Pythagorean theorem we can solve for any of the side lengths of a triangle.
a will be the first side,
b will be the second side,
c will be the hypotenuse
And since the shape is a square, that means a and b will be the same length.
a^2 + b^2 = c^2
a^2 + b^2 = 1024
Since and b are the same, we can combine the left side of the equation to be 2a^2
2a^2 = 1024
Divide both sides by 2
a^2 = 512
Square root both sides
a = 22.6274
We have now solved for the length of one of the sides of the square. Since a square has 4 equal sides, we multiply this by 4 for our answer.
22.6274 x 4 = 90.5096 inches