From Förberedande kurs i matematik 1

Because one of the angles in the triangle is \displaystyle 90^{\circ }, we have a right-angled triangle and can use Pythagoras' theorem to set up a relation between the triangle's sides.

The side of length \displaystyle \text{13} is the hypotenuse in the triangle, and Pythagoras' theorem therefore gives us that

\displaystyle 13^{2}=12^{2}+x^{2}

i.e.

\displaystyle x^{2}=13^{2}-12^{2}

This means that

\displaystyle x=\sqrt{13^{2}-12^{2}}=\sqrt{169-144}=\sqrt{25}=5