Length of Diagonal of Unit Square

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Theorem

The length of a diagonal of a square of side length $1$ is $\sqrt 2$) (the square root of $2$).


Proof

DiagonalOfSquare.png

Two adjacent sides $AB$, $BC$ and the diagonal $AC$ of square $ABCD$ form a right triangle.

The hypotenuse of triangle $\triangle ABC$ can be found by using Pythagoras's Theorem:

$AC^2 = AB^2 + BC^2$

from which:

$AC^2 = 2$

and so:

$AC = \sqrt 2$

$\blacksquare$


Sources