Question

prove that the ratio of diagonal to side in a square equals to root under 2

Answer 1

Let ABCD be the four vertices of the square. Let the length of each side be 'x'.

In square ABCD , AC is the diagonal and two sides of the diagonal are AB and BC.

Here, we got a triangle ABC. By using Pythagoras theorem, find the side AC.

AC² = AB² + BC²

AC² = x² + x²

AC² = 2x²

AC = x√2

In the square ABCD , the ratio of diagonal AC to side AB = x√2 : x

= √2

Hence proved.

Hope u get it!! Sorry for not providing the diagram!