In a right triangle, one of the angles is $90^ ext{o}$ and the lengths of the two legs are equal. If the length of each leg is $4$ units, what is the length of the hypotenuse? Use the Pythagorean theorem which states that for a right triangle with legs of lengths $a$ and $b$, and hypotenuse $c$, the relationship is given by:
$$a^2 + b^2 = c^2$$