The side of one square is equal to 1m, and its diagonal is equal to the side of a second square. Find the diagonal of the second square.

The diagonal of a square forms two 45-45-90 triangles, where the sides of the squares are the legs of the triangles and the diagonal of the square is the hypotenuse of the triangles.

The ratio of the lengths of the leg to the hypotenuse of a 45-45-90 triangle is

1 : sqrt (2)

That means that the diagonal of a square is sqrt (2) times the length of its side.

The first square has side 1 m.

The diagonal is sqrt (2) * 1 m = sqrt (2) m

The diagonal of the first square is the side of the second square.

The second square has side sqrt (2) m

The second square has diagonal sqrt (2) * sqrt (2) m = 2 m