Given a diagonal of a square, /, we are asked to find x. Assuming that x is the length of one side of the square, we can establish a relationship between the diagonal and the side. Illustrate a square and a diagonal drawn across sides:
The result is two right triangles. If x is the length of one side, the two legs of the triangle is x and x. Therefore, the diagonal is the hypotenuse. Expressing / in terms of x:
/^2 = x^2 + x^2
/^2 = 2x^2
/ = √2 x