The first kingdom is rich and powerful, filled with wealthy, prosperous people, the second is humbler, but has its fair share of wealth and power. The third kingdom is struggling and poor, and barely has an army.
The kingdoms eventually go to war over control of the lake, as it's a valuable resource to have. The first kingdom sends 100 of its finest knights, clad in the best armour and each with their own personal squire. The second kingdom sends 50 knights, with fine leather armour and a few dozen squires of their own. The third kingdom sends their one and only knight, an elderly warrior who has long since passed his prime, with his own personal squire.
The night before the big battle, the knights in the first kingdom drink and party into the late hours of the night. The knights in the second kingdom aren't as well off, but have their own supply of grog and drink well into the night.
In the third camp, the faithful squire gets a rope and swings it over the branch of a tall tree, making a noose, and hangs a pot from it. He fills the pot with stew and has a humble dinner with the old knight.
The next morning, the knights in the first two kingdoms are hungover and unable to fight, while the knight in the third kingdom is old weary, unable to get up.
In place of the knights, the squires from all three kingdoms go and fight. The battle lasts long into the night but by the time the dust settled, only one squire was left standing - the squire from the third kingdom.
And it just goes to show you that the squire of the high pot and noose is equal to the sum of the squires of the other two sides.
Original credit to /u/Gaphumbala
Now I'm waiting for a mathematician to post a comment that starts "Actually . . . "
It all depends on what is meant by a "perfect" triangular Lake. If it's a right triangle, then the joke works. But if it's any other type of triangle (e.g. equilateral), there's a pesky 2ab*cosθ term that you need to consider...