From Förberedande kurs i matematik 1

Because one of the angles in the triangle is 90°, we have a right-angled triangle and can use the Pythagorean theorem to set up a relation between the triangle's sides.

The side of length 13 is the hypotenuse in the triangle, and the Pythagorean theorem therefore gives us that

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

i.e.

\displaystyle x^{2}=13^{2}-12^{2}\,\textrm{.}

This means that

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