Question

The ratio of a side and a diagonal of a square is

Answer 1

A diagonal divides a square into two45-45-90 triangles, which have lengths adhering to the ratio of x: x: x√2. Therefore, 4√2 is the correct answer as the diagonal represents the hypotenuse of the triangle. the Pythagorean theorem can also be used: 42+ 42 = c2.
or
A diagonal divides a square into two 45-45-90 triangles, which have lengths adhering to the ratio of x: x: x√2. Therefore, 2 is the correct answer as the diagonal represents the hypotenuse of the triangle. the Pythagorean theorem can also be used: √22+ √22 = c2. 

Answer 2

let the side of square = a
then length of diagonal = a√2 (by Pythagoras)
so the required ratio= 1:√2