<s>[INST] Dr. Lee wants to put a fence around a triangular region in his backyard that is shaped like a right triangle. He wants to fence the region in a way that uses the minimum amount of fencing while enclosing the triangular space formed by the right angle. If the lengths of the legs of the right triangle are given as $a$ and $b$, what is the length of the least amount of fencing needed to enclose the triangle?[/INST]